exfat does not have a dirty bit - not that I know of - only ntfs - and only set if system is hibernating or has Windows Fast Startup enabled.
It was opensourced a couple of years back - so I am fairly certain the kernel module adheres to specification.
If you have problems with data getting courrupted, you may benefit from using a kernel > 6.1 and disable writecache for USB → [root tip] [How To] Disable write cache for USB storage devices
Do not read too much into that - it is and has always been a problem with NTFS in dual-boot environments - and the default answer is always - boot windows and run chkdsk command.
I think that because Linux natively support the NTFS filesystem - users begin to think - hey I can use it for everything - but you cannot - and because it is a reverse engineered driver - it is bound to have issues - it inevitable.