chore: enable TypeScript strict mode and drop dead Payload scripts

The shared base tsconfig had strict off, so null-safety and union narrowing
were not checked. Strict is now on for apps/web with 5 small typing fixes.
check-db.ts and migrate-drafts.js depended on Payload, which is no longer a
dependency, and are removed. CLAUDE.md no longer claims Payload.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>

apps/web/scripts/check-forms.ts

@@ -81,9 +81,11 @@ async function main() {
     }
   });
 
-  page.on("pageerror", (err: Error) => {
+  page.on("pageerror", (err: unknown) => {
     if (currentScannedUrl.includes("showcase")) return;
-    console.error(`  [PAGE EXCEPTION] ${err.message}`);
+    console.error(
+      `  [PAGE EXCEPTION] ${err instanceof Error ? err.message : String(err)}`,
+    );
   });
 
   // Listen to ALL network responses to catch broken assets (404/500)