Remember terminal input mode and restore keyboard shortcut icon

[powerfooI]

Summary

• Restore the historical Lucide Keyboard icon on both two-row shortcut show/hide buttons while keeping their accessible labels and expanded state.
• Remember explicit Composer/Direct radio choices as a browser-local UI preference, surviving panel close/reopen and reload. Invalid or absent preferences default to Composer; storage write failures retain the current page's choice.
• Keep Commands, connection/pane resets, and disconnected fallbacks transient. Retire live input sessions as before; only the explicit Type gesture or terminal interaction activates Direct input.
• Route Type's synchronous focus to the restored mode and cover initial mounting and React StrictMode.

Verification

• bun run format:check, bun run lint, bun run typecheck, bun run typecheck:quick, bun run build:web, and bun run build:site passed.
• bun test web/src scripts: 1,175 passed, 0 failed.
• Real React/Happy DOM lifecycle coverage: 22 cases, 188 assertions, including close/reopen, stored reload state, explicit switches, Commands, initial open/StrictMode, disconnection, connection/pane/generation changes, and stale input callbacks.
• Initial JS gzip: 207,858 / 207,872 bytes; existing budget unchanged.
• Full bun run precommit reached the full-suite test stage: 2,109 passed, 2 skipped, 264 failed. The failure-name set exactly matches the prior Fix composer upload races and desktop downloads #312 baseline in this environment (Unix socket listen and local connection failures); expanded execution did not remove those environment restrictions. GitHub Actions CI run 505 passed on exact head 5bda04a589691d67122eb10aa43a6dfa364b20af, including the complete test:quick suite, formatting, lint, type checks, build/budget checks, and site build.
• Actual iOS Safari/Android keyboard and IME behavior has not been tested on physical devices.

No version, release, or budget changes.