refactor: define module types for NextAuth user/session payloads to eliminate unsafe any castings

[DebasmitaBose0]

Closes #332

Summary

Added proper typings to NextAuth handlers.

Changes Made

• Created type extensions in next-auth.d.ts.
• Removed as any castings in auth.ts.

Testing

• Verified compile status via npx tsc --noEmit.
• Tested authorization callbacks locally.

Impact

Secures the JWT authentication payload verification.

Checklist

• Code follows project standards
• Tested locally
• No unrelated changes included
• Responsive design verified
• Accessibility considered

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