feat(web): make the whole no-workspace composer card the picker trigger

The pick target grows from the read-only textarea to the full capsule:
the card owns the click, its disabled controls let pointer events fall
through, and a dashed l4 stroke with a business-blue hover marks the
affordance (an SVG dash ring — native dashed has a fixed pattern). The
card contains pointerdown so the open picker's outside-close cannot
race the reopen, which flickered the chip's expansion echo.

packages/client/ui-conversation/src/client/skeleton/InputBar.module.css

@@ -102,6 +102,40 @@
   --dsh-scrollbar-thumb-hover: var(--dsw-alias-scrollbar-hover-l2);
 }
 
+/* No-workspace trigger state: dashed l4 stroke marks the card as a pick-a-
+   workspace affordance rather than a live composer; hover answers in the
+   business blue to invite the click. Native `dashed` has a fixed browser
+   pattern, so the stroke is an ::after overlay: theme-token background masked
+   by an SVG dash ring (stroke-width 2 centered on the box edge = 1px visible
+   inside), which keeps the 22px radius and both themes. */
+.cardWorkspaceTrigger {
+  border-color: transparent;
+  cursor: pointer;
+}
+
+.cardWorkspaceTrigger::after {
+  content: '';
+  position: absolute;
+  inset: -1px;
+  border-radius: 22px;
+  background: var(--dsw-alias-border-l4);
+  transition: background-color 100ms ease;
+  -webkit-mask: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg'%3E%3Crect width='100%25' height='100%25' fill='none' rx='22' ry='22' stroke='black' stroke-width='2' stroke-dasharray='4 4'/%3E%3C/svg%3E");
+  mask: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg'%3E%3Crect width='100%25' height='100%25' fill='none' rx='22' ry='22' stroke='black' stroke-width='2' stroke-dasharray='4 4'/%3E%3C/svg%3E");
+  pointer-events: none;
+}
+
+/* Disabled toolbar controls neither receive nor swallow clicks in the trigger
+   state: pointer events fall through to the card's own click handler, making
+   the full capsule one pick target. */
+.cardWorkspaceTrigger :disabled {
+  pointer-events: none;
+}
+
+.cardWorkspaceTrigger:hover::after {
+  background: var(--dsw-alias-state-business-primary);
+}
+
 .accessory {
   display: flex;
   align-items: center;

packages/client/ui-conversation/src/client/skeleton/InputBar.tsx

@@ -467,7 +467,17 @@ export function InputBar({
           {notice.text}
         </div>
       )}
-      <div className={css.card} data-composer-card>
+      {/* Trigger clicks land on the card, not the textarea: the toolbar row's
+          disabled controls swallow clicks otherwise (the CSS state disarms
+          their pointer events), so the WHOLE capsule is the pick target.
+          pointerdown stops here so the Menu's outside-close cannot race the
+          click's reopen (close-then-open flickers the chip's open echo). */}
+      <div
+        className={clsx(css.card, workspaceTrigger && css.cardWorkspaceTrigger)}
+        data-composer-card
+        onClick={workspaceTrigger ? onRequestWorkspace : undefined}
+        onPointerDown={workspaceTrigger ? (e) => { e.stopPropagation() } : undefined}
+      >
         {overlay !== undefined && <div className={css.overlayAnchor}>{overlay}</div>}
         {accessory !== undefined && <div className={css.accessory}>{accessory}</div>}
         {/* One scrollport, two text layers. The hidden mirror renders draft+'\n' and stretches the
@@ -496,7 +506,6 @@ export function InputBar({
               rows={2}
               onChange={onChange}
               onKeyDown={onKeyDown}
-              onClick={workspaceTrigger ? onRequestWorkspace : undefined}
               onSelect={onSelect}
               onCopy={(e) => { onCopyOrCut(e, false) }}
               onCut={(e) => { onCopyOrCut(e, true) }}