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/app/chat/page.tsx

@@ -28,19 +28,19 @@ export default function ChatPage(): ReactElement {
   const [sidebarOpen, setSidebarOpen] = useState(false);
   const [currentConversationId, setCurrentConversationId] = useState<string | null>(null);
 
-  const handleConversationChange = (conversationId: string | null) => {
+  const handleConversationChange = (conversationId: string | null): void => {
     setCurrentConversationId(conversationId);
     // NOTE: Update sidebar when conversation changes (see issue #TBD)
   };
 
-  const handleSelectConversation = async (conversationId: string | null) => {
+  const handleSelectConversation = async (conversationId: string | null): Promise<void> => {
     if (conversationId) {
       await chatRef.current?.loadConversation(conversationId);
       setCurrentConversationId(conversationId);
     }
   };
 
-  const handleNewConversation = (projectId?: string | null) => {
+  const handleNewConversation = (projectId?: string | null): void => {
     chatRef.current?.startNewConversation(projectId);
     setCurrentConversationId(null);
   };