What is the norm for visitors in a rehab /skilled nursing facility?

I'm guessing the OP knows the rules at the facility in question but wants to do a comparison because they seem excessively restrictive.
You can probably search the web to discover any state mandates but I think the only way to know what is happening in specific facilities your area would be to call around to each place and ask.

Each place has their own rules even when in the same state.

One example: If vaccinated, can go to the person's room and visit after being screened. If not vaccinated, can still go visit but have to wear one of their masks and can't be in their room if they have a roommate.

I'm sure that with Covid still hanging around, each facility has different rules set up for visitors, depending on how bad the Covid situation is in their area.
Thankfully though, most are back to allowing visits for family and friends at least twice a week, and some even more than that. Like AlvaDeer suggested, it's always best to contact the facility in question, to see what their rules are.

There is no "norm". You need to check with the facility involved. They will be happy to answer for their own facility.