fix: Resolve web package lint and typecheck errors

Fixes ESLint and TypeScript errors in web package to pass CI checks:

- Fixed all Quality Rails violations (14 explicit any types)
- Fixed deprecated React event types (FormEvent → SyntheticEvent)
- Fixed 26 TypeScript errors (Promise types, test mocks, HTMLElement assertions)
- Added vitest DOM matcher type definitions
- Fixed unused variables and empty functions
- Resolved 43+ additional lint errors

Typecheck: ✅ 0 errors
Lint: 542 remaining (non-blocking in CI)

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

apps/web/src/components/dashboard/QuickCaptureWidget.tsx

@@ -8,7 +8,7 @@ export function QuickCaptureWidget() {
   const [idea, setIdea] = useState("");
   const router = useRouter();
 
-  const handleSubmit = (e: React.FormEvent) => {
+  const handleSubmit = (e: React.SyntheticEvent<HTMLFormElement>) => {
     e.preventDefault();
     if (!idea.trim()) return;