[codex] Fix Gemini web regressions

[yappologistic]

What Changed

• restored the shared traits-picker control props for Gemini so the picker respects shared open state, close handling, and shortcut hints
• kept Gemini model discovery enabled while provider switching is still allowed, and only disable it after another provider has locked the thread
• added shortcut-sheet coverage and keybinding docs for chat.newGemini / Ctrl+Alt+G
• added targeted unit and browser regression tests for the Gemini picker flow, model-query enablement, and shortcut visibility

Why

The recent Gemini support rollout left three web regressions in place:

1. the Gemini traits picker stopped responding to the shared composer state
2. live Gemini models were hidden from the picker unless Gemini was already selected
3. the Gemini new-thread shortcut existed in the keybindings layer but was missing from the shortcuts sheet and docs

This PR keeps the scope tight and focused on polishing the shipped Gemini support without widening into unrelated provider work.

UI Changes

This PR fixes interaction and discoverability regressions in the existing UI rather than introducing a new layout.

• before: the Gemini traits picker did not honor the shared open state / shortcut wiring, and the shortcuts sheet did not show the Gemini thread shortcut
• after: the Gemini traits picker is controlled correctly again, and the shortcuts sheet exposes New Gemini thread with Ctrl+Alt+G

I verified the updated shortcuts dialog in the running web app. I am not attaching screenshots or a video to this PR.

Verification

• cd apps/web && bun run test src/components/chat/composerProviderRegistry.test.tsx src/shortcutsSheet.test.ts src/components/ChatView.logic.test.ts
• cd apps/web && bunx vitest run --config vitest.browser.config.ts src/components/chat/composerProviderRegistry.browser.tsx
• bun fmt
• bun lint (warnings only, no errors)
• bun typecheck

Checklist

• This PR is small and focused
• I explained what changed and why
• I included before/after screenshots for any UI changes
• I included a video for animation/interaction changes