fix: Resolve all ESLint errors and warnings in web package

Fixes all 542 ESLint problems in the web package to achieve 0 errors and 0 warnings.

Changes:
- Fixed 144 issues: nullish coalescing, return types, unused variables
- Fixed 118 issues: unnecessary conditions, type safety, template literals
- Fixed 79 issues: non-null assertions, unsafe assignments, empty functions
- Fixed 67 issues: explicit return types, promise handling, enum comparisons
- Fixed 45 final warnings: missing return types, optional chains
- Fixed 25 typecheck-related issues: async/await, type assertions, formatting
- Fixed JSX.Element namespace errors across 90+ files

All Quality Rails violations resolved. Lint and typecheck both pass with 0 problems.

Files modified: 118 components, tests, hooks, and utilities

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

apps/web/src/components/auth/LogoutButton.tsx

@@ -9,11 +9,14 @@ interface LogoutButtonProps {
   className?: string;
 }
 
-export function LogoutButton({ variant = "secondary", className }: LogoutButtonProps) {
+export function LogoutButton({
+  variant = "secondary",
+  className,
+}: LogoutButtonProps): React.JSX.Element {
   const router = useRouter();
   const { signOut } = useAuth();
 
-  const handleSignOut = async () => {
+  const handleSignOut = async (): Promise<void> => {
     try {
       await signOut();
     } catch (error) {