feat(chat): add sidebar conversation history search

[yovinchen]

Summary

• add a Codex-style search entry beside the sidebar conversation controls
• search persisted conversation titles and message history across workspaces, prioritize the current workspace, and open results directly
• add an optional configurable desktop global shortcut and keep WebUI button-only
• cover search semantics, shortcut registration, and the sidebar integration with tests

Screenshots / preview

Verification

• make check-all: 19 of 21 steps passed locally
• mise exec -- cargo test --workspace --all-targets: 1000 passed, 3 ignored, 0 failed outside the restricted sandbox
• Biome checks passed for all changed TypeScript and JavaScript files
• git diff --check passed

The two local make failures are baseline/environment-only: Shared UI lint reports formatting in three untouched origin/main files, and the sandboxed Rust test step could not perform process and user-directory operations; the same Rust suite passes outside the sandbox.

Closes #741

[github-actions]

PR governance checks passed. Awaiting human review.