fix(remote): stabilize PWA worktree state sync

[SDSLeon]

Summary

• add a main-process Git state service and project snapshots so desktop and PWA clients share one worktree read model
• make remote reconnect, hydration, refresh, and reset flows consistently restore Git summaries and thread state
• harden remote transport with payload interest filtering, size guards, stable timestamps, HTTP compression, and compact image references/previews
• align mobile and renderer worktree controls, image rendering, and floating UI behavior with the synchronized state model

Root cause

The remote PWA assembled worktree and Git state through several independent snapshot and hydration paths. During setup or reconnect, those paths could race, reuse incomplete legacy data, or omit updates, leaving the PWA with stale or missing worktree state. Large inline image and thread payloads also made remote synchronization less reliable.

Impact

PWA sessions now receive stable, bounded state updates and recover the current worktree, Git summary, thread changes, and image content more reliably after initial setup and reconnects.

Validation

• pnpm run typecheck
• pnpm run lint
• pnpm run test — 7,044 passed, 67 skipped
• git diff --check