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/chat/BackendStatusBanner.tsx

@@ -25,7 +25,7 @@ export function BackendStatusBanner() {
     try {
       // NOTE: Implement signOut (see issue #TBD)
       // await signOut();
-    } catch (_error) {
+    } catch (error) {
       // Silently fail - will redirect anyway
       void error;
     }
@@ -63,8 +63,8 @@ export function BackendStatusBanner() {
           />
         </svg>
         <span>
-          {error || "Backend temporarily unavailable."}
-          {retryIn > 0 && <span className="ml-1">Retrying in {retryIn}s...</span>}
+          {_error || "Backend temporarily unavailable."}
+          {_retryIn > 0 && <span className="ml-1">Retrying in {_retryIn}s...</span>}
         </span>
       </div>
       <div className="flex items-center gap-2">

apps/web/src/components/chat/MessageList.tsx

@@ -122,7 +122,7 @@ function MessageBubble({ message }: { message: Message }) {
                 backgroundColor: "rgb(var(--surface-2))",
                 color: "rgb(var(--text-muted))",
               }}
-              title={`Prompt: ${message.promptTokens?.toLocaleString() || 0} tokens, Completion: ${message.completionTokens?.toLocaleString() || 0} tokens`}
+              title={`Prompt: ${message.promptTokens?.toLocaleString() || "0"} tokens, Completion: ${message.completionTokens?.toLocaleString() || "0"} tokens`}
             >
               {formatTokenCount(message.totalTokens)} tokens
             </span>