feat(ui-models): tag the provider rows this deployment declared

A row's stored profile could not tell a hand-declared gateway from a
shipped provider whose models someone narrowed — both look identical from
outside the adapter — so the Models page had no way to mark the routes a
deployment added itself.

The directory entry now carries `declared`, answered by the owning adapter
against its own installed catalog, and the page renders a Custom tag from
it. Absence stays "this adapter draws no such distinction" rather than
"shipped", so a route no adapter claims is labelled neither way.

Also records the default-route work's Agent Note and the e2e evidence for
all three changes: the composer switch writing the section, and the Models
page declaring a route with its own reasoning effort.

packages/llm/llm-pi-ai/src/index.ts

@@ -92,11 +92,21 @@ function registrationFacts(profiles: ReadonlyMap<string, ResolvedPiAiProviderPro
 function directoryEntries(
   profiles: ReadonlyMap<string, ResolvedPiAiProviderProfile>,
 ): LlmConfigurableProvider[] {
+  const catalog = new Set(catalogProviderIds())
   const entries = new Map<string, LlmConfigurableProvider>()
   const declare = (provider: string, displayName: string): void => {
-    entries.set(provider, { provider, displayName, settingsNs: NS, settingsPath: ['providers', provider] })
+    entries.set(provider, {
+      provider,
+      displayName,
+      settingsNs: NS,
+      settingsPath: ['providers', provider],
+      // Membership of the installed catalog, not of the settings document:
+      // narrowing a shipped provider's models stores a profile too, and that
+      // route is still one pi-ai knows.
+      declared: !catalog.has(provider),
+    })
   }
-  for (const provider of catalogProviderIds()) declare(provider, provider)
+  for (const provider of catalog) declare(provider, provider)
   for (const [provider, profile] of profiles) declare(provider, profile.displayName)
   return [...entries.values()]
 }