H1-B Transfer after Booking an appointment

I am working for Employer A for a Client X and my client has agreed to file for my H1-B Transfer application to hire me as a full time employee. I have a consular appointment scheduled to get my H1-B VISA Stamped with Employer A’s H1-B approval notice. If my client files for my transfer application and if it is approved before my appointment date am I allowed to fill out a new DS-160 form with the Client’s H1-B transfer approval details and still attend to the same appointment or would I have to schedule a new appointment with the new DS-160 information?

Yes, you can use same appointment and submit a new DS-160 before the appointment. Carry both old and new DS-160 to your appointment amd all H1B documents related to the new employer.

How do I submit my new DS-160 to the existing appointment? Just update my usatravel docs profile with the new DS-160 number and carry the copies to my dropbox appointment?

Yes that is exactly what you can do.