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/domains/DomainSelector.test.tsx

@@ -88,7 +88,7 @@ describe("DomainSelector", (): void => {
     const onChange = vi.fn();
     render(<DomainSelector domains={mockDomains} value="domain-1" onChange={onChange} />);
 
-    const select = screen.getByRole("combobox");
+    const select = screen.getByRole("combobox") as HTMLSelectElement;
     expect(select.value).toBe("domain-1");
   });