feat: implement M3 multi-browser support (Firefox, Edge, Safari)

Add browser abstraction layer (compat.ts) that normalizes Chrome/Firefox/
Edge/Safari extension APIs behind a unified promise-based interface.
Replace all direct chrome.* calls with compat layer across service worker,
sync engine, badge, storage, popup, and options modules.

- Browser-specific manifests in manifests/ (Firefox MV3 with gecko settings,
  Edge/Safari variants)
- Multi-target build system: `npm run build` produces all four browser
  builds in build/<browser>/
- Per-browser build scripts: build:chrome, build:firefox, build:edge, build:safari
- Auto-detects browser at runtime for platform-specific device registration
- All 38 existing tests pass, typecheck clean

Co-Authored-By: Paperclip <noreply@paperclip.ing>

extension/package.json

@@ -5,7 +5,11 @@
   "description": "CookieBridge Chrome Extension — cross-device cookie sync with E2E encryption",
   "scripts": {
     "build": "node esbuild.config.mjs",
-    "watch": "node esbuild.config.mjs --watch",
+    "build:chrome": "node esbuild.config.mjs --browser=chrome",
+    "build:firefox": "node esbuild.config.mjs --browser=firefox",
+    "build:edge": "node esbuild.config.mjs --browser=edge",
+    "build:safari": "node esbuild.config.mjs --browser=safari",
+    "watch": "node esbuild.config.mjs --watch --browser=chrome",
     "typecheck": "tsc --noEmit"
   },
   "dependencies": {