The amount of tracking the intrusiveness of it highly depends on the type of management they used.

MAM or work profiles are most often used for personal devices and it grants the employer the ability to only manage specific apps and or profile.

MDM enrollment is used for corporate owned devices and is more capable.

Here is some documentation for MS Intune, it will be slightly different for other providers but it will be roughly the same: https://learn.microsoft.com/en-us/mem/intune/apps/android-deployment-scenarios-app-protection-work-profiles

If it’s for work related apps, they owe you a device to run it on.

Absolutely.