test: typecheck test files in CI; drop mock-only test; richer chrome mock

- typecheck now also runs tsc over tsconfig.test.json (test files were
  never type-checked before).
- Delete tests/unit/background.test.ts, which only asserted the vitest
  chrome mock's own behavior — every remaining test imports production
  code from src/lib.
- Baseline mock gains runtime.id, storage.session/remove, contextMenus,
  and tabs.sendMessage.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

tests/unit/setup.ts

@@ -1,9 +1,15 @@
-// Mock Chrome extension APIs
+// Baseline Chrome extension API mock. Individual tests may rebuild
+// global.chrome to control specifics (e.g. runtime.id presence).
 global.chrome = {
   storage: {
     local: {
       get: vi.fn((keys, cb) => cb({})),
       set: vi.fn((data, cb) => cb && cb()),
+      remove: vi.fn((keys, cb) => cb && cb()),
+    },
+    session: {
+      get: vi.fn((keys, cb) => cb({})),
+      set: vi.fn((data, cb) => cb && cb()),
     },
     sync: {
       get: vi.fn((keys, cb) => cb({})),
@@ -11,10 +17,24 @@ global.chrome = {
     },
   },
   runtime: {
+    id: 'test-extension-id',
     sendMessage: vi.fn(),
     onMessage: {
       addListener: vi.fn(),
     },
+    onInstalled: {
+      addListener: vi.fn(),
+    },
     openOptionsPage: vi.fn(),
   },
+  contextMenus: {
+    create: vi.fn(),
+    removeAll: vi.fn((cb) => cb && cb()),
+    onClicked: {
+      addListener: vi.fn(),
+    },
+  },
+  tabs: {
+    sendMessage: vi.fn(),
+  },
 } as any;