It sounds like your brakes are pulsating.
Did you get a chance to have look at the brake rotors?
What you describing sounds like you might have warped rotors.
So when you apply the brake you feel the unevenness of the rotors, as the high spots and low spots on the rotors gives you the back and forth feel.
You will have to do a rotor runout check to see if they are the issue. I have attached the testing procedure (look bellow). Also includes the specifications.
This is few links you might find helpful:
Please let me know of any questions.
Images (Click to enlarge)
Tuesday, July 20th, 2021 AT 3:27 PM