We have thousands of Macs in use where I work and those Sony headphones are the primary full over ear headphones that are offered to us to use with the work computers. I have a set. Our Macs are all on 12.6.2 and 13.1 and the headphones seem to work very well without stuttering (with bluetooth). The leads me to suspect that there is something installed in your system that might conflict with the headphones normal operation. That would also be consistent with what you report about no problems with Windows or Android devices.
In addition to the good suggestion to start in Safe Mode and retest, you could download Etrecheck and run it and post the output here using the Additional text button below. Lots of experts can then go through that Etrecheck report (which provides only diagnostic information about your device, no identifying information, which you can check yourself before posting ... Etrecheck is also open source software, it has nothing to hide) and maybe see if there is something installed that might be interfering.