fix(flow-chat): refine ChatInput mode menus

[GCWing]

Summary

• simplify the ChatInput Harness row to show the current mode icon and label, and open the mode picker directly
• make started-session mode changes explicitly create a new session and remove custom Agent creation from the add menu
• present native model and reasoning choices as persistent click-open side submenus with overlay-host positioning and keyboard focus restoration

Validation

• focused Web UI tests: 8 files, 80 tests passed
• pnpm run i18n:audit
• pnpm run appearance:contract-audit
• pnpm run motion:audit
• targeted ESLint for ChatInput, HarnessProfileSelector, and ModelSelector
• git diff --check

The full Web UI type-check reached TypeScript and was blocked only by the existing missing @/generated/api module in websocket-adapter.ts and ConfigAPI.ts; no changed-file type error was reported.

Scope

• no browser or mock visual validation, following the repository instruction
• presentation-only Web UI behavior; remote workspace, remote control, Peer Device Mode, and Detached Dispatch were not separately exercised