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/app/(authenticated)/tasks/page.test.tsx

@@ -5,7 +5,7 @@ import TasksPage from "./page";
 // Mock the TaskList component
 vi.mock("@/components/tasks/TaskList", () => ({
   TaskList: ({ tasks, isLoading }: { tasks: unknown[]; isLoading: boolean }) => (
-    <div data-testid="task-list">{isLoading ? "Loading" : `${tasks.length} tasks`}</div>
+    <div data-testid="task-list">{isLoading ? "Loading" : `${String(tasks.length)} tasks`}</div>
   ),
 }));