In the absence of native Linux software that allows you to configure the properties of your mouse, I would suggest booting up a Windows2Go install and then configuring your mouse there. As long as your mouse will save those settings to the device itself, they should persist when you use Bazzite.
My personal recommendation is to use Razer mice since the OpenRazer project works very well on Linux and should solve many of these problems, contingent on whether you are using a Razer mouse that is supported.
You can run sudo libinput debug-events in your terminal of choice(Ptyxis is the default though), move the pointer aronud and count the time between each event. If the time between each POINTER_MOTION event is 1ms(0.001s) then you have 1000Hz polling rate.
Press Ctrl+C in the terminal afterwards to stop the tool.
I used to use Razer Viper 8K (8000HZ) mice, but Endgame 8K is wildly better.(also newer)
The biggest question in this case, is the fact that i want to actually see that Bazzite is pulling the 8000hz, from the mouse, since i must say i clearly feel the latency difference on the Desktop of Bazzite, compared to Win11..