fix(web): keep ineligible message forks disabled

apps/web/tests/snapshots/bash-abort-row/ui.expected.md

@@ -7,8 +7,9 @@
 - text: "Run two shell commands: wait for cancellation, then write skipped.txt. {{date}} {{clock}}"
 - button "Copy":
   - img
-- button "Branch into a new conversation":
+- button "Branch into a new conversation" [disabled]:
   - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img

apps/web/tests/snapshots/code-mode-round/ui.expected.md

@@ -7,6 +7,9 @@
 - text: "Using ONE run_code program: run bash `echo CODE_ROUND_OK`, then read the file missing.txt catching its error in the program. Return an object with both outcomes. Then reply DONE and stop. {{clock}}"
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img

apps/web/tests/snapshots/cordis-tool-round/ui.expected.md

@@ -7,6 +7,9 @@
 - text: "Use only Cordis tools. First call cordis_inspect with what \"temporary\". Then call cordis_mount with this exact code: \"return { name: \\\"snapshot-noop\\\", apply(ctx) {} }\". Read its returned id and call cordis_unmount with that exact id. After all three calls succeed, reply exactly CORDIS_UI_DONE and stop. {{clock}}"
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img

apps/web/tests/snapshots/fresh-round-trip/ui.expected.md

@@ -7,6 +7,9 @@
 - text: "Use the bash tool to run exactly: echo WEB_E2E_OK. Then reply with the single word DONE and stop. {{clock}}"
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img

apps/web/tests/snapshots/lifecycle-chrome/reloaded.expected.md

@@ -7,6 +7,9 @@
 - text: Reply with the single word LIGHTHOUSE and stop. {{clock}}
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img

apps/web/tests/snapshots/live-interactions/cancel.expected.md

@@ -7,6 +7,9 @@
 - text: Reply with a one-sentence description of event sourcing, then stop. {{clock}}
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img

apps/web/tests/snapshots/live-interactions/error-auth.expected.md

@@ -7,6 +7,9 @@
 - text: Reply with a one-sentence description of event sourcing, then stop. {{clock}}
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img

apps/web/tests/snapshots/live-interactions/loading.expected.md

@@ -7,6 +7,9 @@
 - text: Reply with a one-sentence description of event sourcing, then stop. {{clock}}
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img

apps/web/tests/snapshots/live-interactions/retry.expected.md

@@ -7,6 +7,9 @@
 - text: Reply with a one-sentence description of event sourcing, then stop. {{clock}}
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img

apps/web/tests/snapshots/message-actions/ui.expected.md

@@ -8,6 +8,9 @@
 - button "Copy":
   - img
 - tooltip "Copy"
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Think The user wants me to read a.txt and b.txt, then reply with \"DONE\". Let me do both reads in parallel.":
   - img
   - img
@@ -15,7 +18,9 @@
 - paragraph: I will read both files before answering.
 - button "Copy":
   - img
-- text: 7/25 {{clock}}
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn 7/25 {{clock}}
 - button "Read a.txt":
   - img
   - img
@@ -33,6 +38,9 @@
 - text: Stopped Now give the final answer. 7/25 {{clock}}
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - paragraph: DONE
 - button "Copy":
   - img

apps/web/tests/snapshots/plan-review/approved.expected.md

@@ -8,6 +8,9 @@
 - text: "plan Plan mode on. Use /plan off to leave. Plan a small change: add a --greeting flag to a CLI. Do not read or write any files. Call exit_plan_mode with a short plan of at most five bullet points. Once the plan is approved, reply with the single word DONE and stop. {{clock}}"
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img

apps/web/tests/snapshots/question-composer/answered.expected.md

@@ -7,6 +7,9 @@
 - text: "Use the ask_user_question tool to ask me exactly one question with id \"color\", question \"Which color do you prefer?\", header \"Pick one\", and two options: label \"Blue\" with description \"A cool recessive hue that reads as calm and trustworthy in long reading sessions and dense dashboards.\", and label \"Green\" with description \"A restful mid-spectrum hue with the highest perceived brightness, easiest on the eye over long sessions.\" After I answer, reply with the single word DONE and stop. {{clock}}"
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img

apps/web/tests/snapshots/queue-actions/collapsed.expected.md

@@ -7,6 +7,9 @@
 - text: Reply with a one-sentence description of event sourcing, then stop. {{clock}}
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img

apps/web/tests/snapshots/queue-actions/editing.expected.md

@@ -7,6 +7,9 @@
 - text: Reply with a one-sentence description of event sourcing, then stop. {{clock}}
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img

apps/web/tests/snapshots/queue-actions/preserved.expected.md

@@ -7,6 +7,9 @@
 - text: Reply with a one-sentence description of event sourcing, then stop. {{clock}}
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img
@@ -20,6 +23,9 @@
 - text: {{clock}} Edited queue item {{clock}}
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - paragraph: partial
 - status: Deep diving...
 - list:

apps/web/tests/snapshots/queue-actions/ui.expected.md

@@ -7,6 +7,9 @@
 - text: Reply with a one-sentence description of event sourcing, then stop. {{clock}}
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img

apps/web/tests/snapshots/seeded-history/command-row.expected.md

@@ -7,6 +7,9 @@
 - text: "Use the read tool twice in one assistant message: read a.txt and b.txt. Then reply with the single word DONE and stop. 7/25 {{clock}}"
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Think The user wants me to read a.txt and b.txt, then reply with \"DONE\". Let me do both reads in parallel.":
   - img
   - img

apps/web/tests/snapshots/seeded-history/ui.expected.md

@@ -7,6 +7,9 @@
 - text: "Use the read tool twice in one assistant message: read a.txt and b.txt. Then reply with the single word DONE and stop. 7/25 {{clock}}"
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Think The user wants me to read a.txt and b.txt, then reply with \"DONE\". Let me do both reads in parallel.":
   - img
   - img

apps/web/tests/snapshots/steering/mid-steer.expected.md

@@ -7,6 +7,9 @@
 - text: Use the ask_user_question tool to ask me exactly one question with id "checkpoint", question "Ready to continue?", header "Checkpoint", and options labeled "Yes" and "No". After I answer, reply with one short sentence acknowledging my answer and stop. {{clock}}
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img

apps/web/tests/snapshots/steering/settled.expected.md

@@ -7,6 +7,9 @@
 - text: Use the ask_user_question tool to ask me exactly one question with id "checkpoint", question "Ready to continue?", header "Checkpoint", and options labeled "Yes" and "No". After I answer, reply with one short sentence acknowledging my answer and stop. {{clock}}
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img
@@ -22,6 +25,9 @@
 - text: "Interjection: include the word BANANA in your final reply. {{clock}}"
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Think The user selected \"Yes\" and wants me to include the word \"BANANA\" in my final reply. Let me acknowledge their answer.":
   - img
   - img

apps/web/tests/snapshots/subagent-conversation/ui.expected.md

@@ -12,6 +12,9 @@
 - text: Explain event sourcing in one sentence. {{clock}}
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img
@@ -28,6 +31,9 @@
 - text: {{clock}} Now give the same explanation to a human reader. {{clock}}
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Think The user is asking for a one-sentence description of event sourcing. This is a straightforward knowledge question that doesn't require any skill loading or tool calls.":
   - img
   - img

apps/web/tests/snapshots/web-search-round/ui.expected.md

@@ -7,6 +7,9 @@
 - text: Use web_search to search exactly "DeepSeek Harness snapshot search". Then reply exactly SEARCH_DONE and stop. {{clock}}
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img