Bluetooth audio is a mess of compromise. The default sbc codec is basically fine for low latency but the parameters are all pretty terrible. Everyone uses the same few default parameters which neither give particularly high quality (especially for two way audio which was designed to be compatible with phone quality), nor low latency (especially for the high quality a2dp profile). One issue is that the designs/defaults haven’t really been updated since about 2000, and the parameters are very hard to change, typically the OS’s preference is hardcoded somewhere (also, whichever device initiates the connection gets to choose the parameters so even if you configured your computer to choose “better” parameters, it would all be for naught if you let the headphones connect to the computer rather than the other way round). The other issue is that Bluetooth is quite severely bandwidth constrained and higher bandwidth could theoretically give lower latency.
I do play some rhythm games (LLSIF, deresute, mirishita) on Android. The difference between "only adds 30ms" and plugging my headphones directly to the headphone jack is the difference between unplayable and playable. The games do have a latency compensation setting (with a calibration procedure), but compensation is no substitute for the real thing: Low latency.
AptX low latency codec adds only 40ms max.
Just buy headphones with good low latency support. They aren't even expensive anymore.