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>

tsconfig.test.json

@@ -1,7 +1,7 @@
 {
   "extends": "./tsconfig.json",
   "compilerOptions": {
-    "types": ["vitest/globals"]
+    "types": ["chrome", "vitest/globals"]
   },
   "include": [
     "tests/**/*"