Add debug logging to file and fix blank startup screen

- Added write_log Tauri command that writes to frontend.log in app data dir
- App.svelte now logs each startup step (Tauri import, sidecar check, launch)
- Startup overlays use inline styles as fallback so they're visible even if
  CSS variables fail to load
- Debug status shown on the checking/connecting screens
- Rust side logs startup info to app.log (resource dir, data dir)

Log files location: %APPDATA%/net.anhonesthost.local-transcription/ (Windows)
or ~/Library/Application Support/net.anhonesthost.local-transcription/ (macOS)

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

src-tauri/Cargo.toml

@@ -24,3 +24,4 @@ futures-util = "0.3"
 zip = { version = "2", default-features = false, features = ["deflate"] }
 bytes = "1"
 tokio = { version = "1", features = ["full"] }
+chrono = "0.4"