Yes, the booster is most likely the problem, here is a guide to help and instructions in the images below to help you change it out:
There are two primary components you might want to focus on: the master cylinder and the brake booster.
Faulty Master Cylinder: Since you recently replaced the master cylinder and the problem arose, it's possible the new master cylinder could be faulty. Though not common, it does happen. In your case, since the brakes are locking up, the issue could be with the master cylinder not properly releasing pressure when the brake pedal is released. It could also be an issue with incorrect installation or an incorrect part, but given your thorough approach, which seems less likely.
Brake Booster: If brake fluid has gotten into the brake booster from the failing master cylinder, it could cause problems with the vacuum assist, resulting in excessive brake pressure and leading to the symptoms you're describing. If you suspect this is the case, the booster will need to be replaced, as it's very difficult to effectively clean brake fluid out of a booster.
Check out the images (below). Please let us know if you need anything else to get the problem fixed.
Images (Click to enlarge)
Thursday, May 25th, 2023 AT 4:44 PM