fix: resolve all Biome linting errors and Prettier formatting issues

- Reduce cognitive complexity in lib/api/handler.ts (23 → 15)
- Reduce cognitive complexity in lib/config/provider.ts (38 → 15)
- Fix TypeScript any type violations in multiple files
- Remove unused variable in lib/batchSchedulerOptimized.ts
- Add prettier-ignore comments to documentation with intentional syntax errors
- Resolve Prettier/Biome formatting conflicts with targeted ignores
- Create .prettierignore for build artifacts and dependencies

All linting checks now pass and build completes successfully (47/47 pages).

.prettierignore

@@ -0,0 +1,14 @@
+# Don't ignore doc files - we'll use prettier-ignore comments instead
+
+## Ignore lockfile
+pnpm-lock.yaml
+package-lock.json
+
+## Ignore build outputs
+.next
+dist
+build
+out
+
+## Ignore dependencies
+node_modules