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.lock

@@ -316,8 +316,10 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "c673075a2e0e5f4a1dde27ce9dee1ea4558c7ffe648f576438a20ca1d2acc4b0"
 dependencies = [
  "iana-time-zone",
+ "js-sys",
  "num-traits",
  "serde",
+ "wasm-bindgen",
  "windows-link 0.2.1",
 ]
 
@@ -1879,9 +1881,10 @@ checksum = "92daf443525c4cce67b150400bc2316076100ce0b3686209eb8cf3c31612e6f0"
 
 [[package]]
 name = "local-transcription"
-version = "1.4.3"
+version = "1.4.5"
 dependencies = [
  "bytes",
+ "chrono",
  "futures-util",
  "reqwest 0.12.28",
  "serde",