fix(app): preserve composer caret after requests

[Hona]

Summary

• persist the live contenteditable cursor before request docks unmount the composer
• restore the saved cursor synchronously before the browser inserts the first printable key
• cover a moved draft caret across question-dock removal

Verification

• focused request-dock regression: 5/5 repeated runs
• full request-dock regression suite: 3 passed
• app typecheck
• E2E typecheck
• repository pre-push typecheck: 30 tasks passed

[Copilot]

Pull request overview

This PR fixes a session composer UX regression where the contenteditable caret position could be lost when request docks temporarily unmount the composer, ensuring the caret is restored before the next printable key is inserted.

Changes:

• Persist the latest contenteditable caret position into prompt state on editor blur.
• When auto-focusing the composer on the first printable keypress, also restore the caret to the saved position (or prompt end).
• Add an E2E regression test that exercises caret preservation across question-dock mount/unmount.

Reviewed changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated no comments.

File	Description
packages/app/src/pages/session.tsx	Restores the prompt editor caret when auto-focusing the composer in the document keydown handler.
packages/app/src/components/prompt-input.tsx	Persists the current caret position to the prompt store on blur so it can be restored after unmount/remount.
packages/app/e2e/regression/session-request-docks.spec.ts	Adds a regression test verifying the caret is restored before typing after a request dock closes.

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