perf(web): typing no longer re-renders the traits picker or attach button

The traits picker took the whole prompt to detect Ultrathink, so every
keystroke re-rendered it. It now takes the three-state Ultrathink reading
it renders from, and receives the live prompt only when a pick edits it.
The attach button's add-attachments handler closed over the cursor
through the non-stable insert helpers; it now calls their stable forms.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
ec8a0878b4Julius Marminge committed on 10/21/2026, 7:04:32 PMparent9179178

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