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/hooks/useWebSocket.test.tsx

@@ -17,14 +17,14 @@ describe("useWebSocket", (): void => {
     mockSocket = {
       on: vi.fn((event: string, handler: (...args: unknown[]) => void) => {
         eventHandlers[event] = handler;
-        return mockSocket as Socket;
+        return mockSocket;
       }) as unknown as Socket["on"],
       off: vi.fn((event?: string) => {
         if (event && Object.hasOwn(eventHandlers, event)) {
           // eslint-disable-next-line @typescript-eslint/no-dynamic-delete
           delete eventHandlers[event];
         }
-        return mockSocket as Socket;
+        return mockSocket;
       }) as unknown as Socket["off"],
       connect: vi.fn(),
       disconnect: vi.fn(),