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/dashboard/QuickCaptureWidget.tsx

@@ -4,11 +4,11 @@ import { useState } from "react";
 import { Button } from "@mosaic/ui";
 import { useRouter } from "next/navigation";
 
-export function QuickCaptureWidget() {
+export function QuickCaptureWidget(): React.JSX.Element {
   const [idea, setIdea] = useState("");
   const router = useRouter();
 
-  const handleSubmit = (e: React.SyntheticEvent<HTMLFormElement>) => {
+  const handleSubmit = (e: React.SyntheticEvent<HTMLFormElement>): void => {
     e.preventDefault();
     if (!idea.trim()) return;
 
@@ -18,7 +18,7 @@ export function QuickCaptureWidget() {
     setIdea("");
   };
 
-  const goToTasks = () => {
+  const goToTasks = (): void => {
     router.push("/tasks");
   };