Mouse stutter (125 HZ polling rate) cause has been found, Devs please read.
The mouse stutter issue that many have been experiencing was previously found (thread here) to be cause by the game using a 125 hz mouse polling rate. However, there has been a new discovery, the 125 hz mouse polling rate is caused by Windows 11 detecting Battlefield 6 as a background app. (Windows 11 limits background apps to a 125 hz polling rate).
A temporary solution to eliminate this issue is by doing a registry fix to get Windows 11 to ignore the 125 hz polling rate for background processes. (Reddit thread here).
I have personally tested the fix and it eliminated my mouse stutter. As I am using a 180hz OLED screen, the stutter was very prominent due to the high response rates that an OLED provides.
I hope this information will be useful to the devs in solving this issue, or help others who have been frustrated with this issue for some time.