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/src/options/options.ts

@@ -1,24 +1,19 @@
 /**
  * Options page script — manages extension settings.
+ * Uses the browser-agnostic compat layer.
  */
+import { runtime, storage } from "../lib/compat";
+
 export {};
 
 // --- Messaging helper ---
 
-function sendMessage(type: string, payload?: unknown): Promise<any> {
-  return new Promise((resolve, reject) => {
-    chrome.runtime.sendMessage({ type, payload }, (response) => {
-      if (chrome.runtime.lastError) {
-        reject(new Error(chrome.runtime.lastError.message));
-        return;
-      }
-      if (response?.error) {
-        reject(new Error(response.error));
-        return;
-      }
-      resolve(response);
-    });
-  });
+async function sendMessage(type: string, payload?: unknown): Promise<any> {
+  const response = await runtime.sendMessage({ type, payload });
+  if (response?.error) {
+    throw new Error(response.error);
+  }
+  return response;
 }
 
 // --- Elements ---
@@ -59,7 +54,7 @@ let blacklist: string[] = [];
 // --- Load Settings ---
 
 async function loadSettings() {
-  const state = await chrome.storage.local.get(null);
+  const state = await storage.get(null);
 
   optDeviceName.textContent = state.deviceName || "—";
   optDeviceId.textContent = state.deviceId || "—";
@@ -168,7 +163,7 @@ btnAddBlacklist.addEventListener("click", () => {
 
 // Save
 btnSave.addEventListener("click", async () => {
-  await chrome.storage.local.set({
+  await storage.set({
     serverUrl: optServerUrl.value.trim(),
     connectionMode: optConnectionMode.value,
     pollIntervalSec: parseInt(optPollInterval.value),
@@ -247,7 +242,7 @@ btnClearData.addEventListener("click", async () => {
     return;
   }
   await sendMessage("LOGOUT");
-  await chrome.storage.local.clear();
+  await storage.clear();
   alert("All data cleared.");
   window.close();
 });