Fix server compile: download PDF to .build dir, prevent artifact sync to Overleaf

The root cause of server compile failures was that output.pdf was being
saved into the synced project directory, causing FileSyncBridge to upload
it back to Overleaf as a project file. CLSI then failed because it found
an existing output.pdf blocking its compilation output.

Changes:
- Save compile artifacts (PDF, synctex.gz) to .build/ subdirectory instead
  of the synced project root — .build is a dotfile dir ignored by chokidar
- Add pdf/pdfxref/stderr/stdout/chktex to FileSyncBridge ignore patterns
- Add rootResourcePath to compile request body (matches Overleaf web client)
- Implement PDF download with fallback via direct build ID URL construction
- Add server compile handler, compile dropdown menu, PDF save button
- Fix resolved comment highlight flash on startup (null initial state)
- Fix EPIPE crash on startup when stdout/stderr is closed
- Fix synctex inverse search to use relative paths via OT doc join

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

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