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 <[email protected]>

apps/web/src/test/setup.d.ts

@@ -0,0 +1,13 @@
+/**
+ * Type declarations for test environment
+ */
+
+import type { TestingLibraryMatchers } from "@testing-library/jest-dom/matchers";
+import type { Assertion, AsymmetricMatchersContaining } from "vitest";
+
+declare module "vitest" {
+  // eslint-disable-next-line @typescript-eslint/no-empty-object-type
+  interface Assertion<T = unknown> extends TestingLibraryMatchers<T, void> {}
+  // eslint-disable-next-line @typescript-eslint/no-empty-object-type
+  interface AsymmetricMatchersContaining extends TestingLibraryMatchers<unknown, void> {}
+}