Looking at the Villager, you can see if they are Working, Staying, Following, etc, but if you look at the UI of the Villager, it always shows as Jobless.

Also noticed that if you have someone follow you or stay, when you tell them to move freely and they were a worker, they no longer show as working until you tell them to work again.
Forge: 1.19.2 - 43.1.33
MCA: 7.3.21

A chore is not a profession. If you interrupt the chore they will not continue working since they don't really remember their work place. Chores are still weird.