refactor(web): ChatView's right panel lives in its own component

The inline and sheet layouts shared one long prop list, written out twice.
The panel's width also follows a resize drag every frame; keeping that state
in the panel stops the drag from re-rendering ChatView.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
9c5f157e3dJulius Marminge committed on 10/21/2026, 7:46:48 AMparentff41fc5

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