fix: use session auth for admin APIs

[nickita-khylkouski]

Summary

• replace the custom admin API Authorization-header gate with NextAuth server session validation
• keep page-level admin protection in middleware without blocking session-authenticated API calls
• reuse the authenticated user lookup across admin profile and post routes

Verification

• npm run lint -- --file lib/admin-auth.ts --file middleware.ts --file app/api/admin/route.ts --file app/api/admin/post/route.ts --file 'app/api/admin/post/[id]/route.ts'
• npx tsc --noEmit
• npm run build

Closes #31

[vercel]

@nickita-khylkouski is attempting to deploy a commit to the safvantsy's projects Team on Vercel.

A member of the Team first needs to authorize it.

[nickita-khylkouski]

Local verification passed:

• npm run lint -- --file lib/admin-auth.ts --file middleware.ts --file app/api/admin/route.ts --file app/api/admin/post/route.ts --file 'app/api/admin/post/[id]/route.ts'
• npx tsc --noEmit
• npm run build

The Vercel check is blocked by fork deployment authorization, not by the build.