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/tsconfig.json

@@ -2,6 +2,7 @@
   "extends": "@mintel/tsconfig/nextjs.json",
   "compilerOptions": {
     "baseUrl": ".",
+    "strict": true,
     "paths": {
       "@/*": ["./*"],
       "@payload-config": ["./payload.config.ts"]