Sounds like your old belt had hit EoL and one or more of the reinforcing fibres were failing.
First thing would be to do the X and Y belt calibration (obligatory e-book link here Dimensional accuracy - Shapeoko CNC A to Z ) and make sure your new belts are calibrated to the correct steps / mm.
I’d suggest that you actually measure the belt tensions so you can track them properly, and balance the two Y belts properly if you’re concerned with precision
I will say that my measurements say that the belt system can deliver really quite surprising precision. I can get within 0.1mm when I really try. The belts do limit the speed of cutting but are way better than leadscrews in achievable precision if you rough then finish so, no you don’t need to replace the controller, motors, belts with ballscrews and rails just to get accurate cuts.
HTH