feat(web): add guarded branch switching to chat input

[bobleer]

Summary

• Make the branch chip above the chat input open a searchable branch switcher.
• Detect checkout conflicts caused by local changes, show affected files and diff stats, and support commit-then-switch.
• Keep managed worktree and detached-dispatch branch labels read-only, and move the switcher under the Git feature owner.

Type and Areas

Type: Feature / UI/UX / test

Areas: Web UI, Git tooling, internationalization

Motivation / Impact

Users can switch ordinary workspace branches directly from the chat input strip. When checkout would overwrite local changes, the UI explains which files block the switch and offers a safe commit-and-retry path without creating duplicate commits on retry.

Verification

• Node 22.23.2: npx --yes node@22.23.2 /Users/liwenbo/.npm-global/lib/node_modules/pnpm/bin/pnpm.mjs --dir src/web-ui run test:run — 579 test files and 4184 tests passed.
• pnpm --dir src/web-ui exec vitest run --maxWorkers=50% src/flow_chat/components/ChatInputWorkspaceStripLayout.test.ts src/tools/git/components/branchSwitchFailure.test.ts src/tools/git/components/BranchQuickSwitch.test.tsx src/flow_chat/components/ChatInputWorkspaceStrip.test.tsx — 61 tests passed.
• pnpm run check:web — passed.
• pnpm run i18n:audit — passed with 0 warnings.
• git diff --check — passed.

Reviewer Notes

Rebased onto upstream/1.0.0-explore at cb87d9c6e. Local UI behavior was exercised. Remote workspace and Peer Device Mode were not exercised end to end; the implementation uses the existing routed Git service rather than direct host APIs. Managed worktrees and detached dispatches remain explicitly read-only in this surface.

Checklist

• This PR is focused and does not include secrets, temporary prompts, generated scratch files, or unrelated artifacts.
• Relevant verification is recorded above, or skipped checks are explained.
• User-facing strings, docs, and locales are updated where applicable.