feat(git): add local branch workflows to new sessions

[lucas77778]

Summary

• add searchable branch selection and quick branch creation to the new-session flow
• make branch choice independent from Local / Worktree execution mode
• safely preflight Local branch switches, show overlapping changed files and line statistics, and support commit-and-continue
• keep Worktree mode isolated from the original checkout and add wire, SDK, engine, mock, cache invalidation, and i18n support
• keep the branch search icon and text in separate InputGroup layout slots so they cannot overlap

Linear: CODE-527

Verification

• pnpm check:ci
• pnpm test — 300 test files / 2408 tests passed; 1 file / 1 test skipped
• pre-commit hooks
• git diff --check
• observed the complete branch search, creation, Local / Worktree, conflict, and commit-and-continue flow in the mock webview
• visually rechecked the search field after merging current master; icon and placeholder have a measured 4px gap with no clipping or overlap

Checklist

• pnpm check:ci and pnpm test both pass (plus cargo fmt / clippy / test for Rust changes)
• I ran the affected surface and observed the change working
• If a wire message changed: WIRE_PROTOCOL_VERSION is bumped
• New code and assets are my own work, or their origin and license compatibility are noted above
• Docs and comments are updated where behavior changed

[linear-code]

CODE-527

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