What do I do about the Senior Living community where my mom resides? They shut down the dining room claiming they can’t hire enough servers.

Call the admin and demand a refund for not providing the services you are paying for. The package you bought including dining room services.

My Mom was in a 39 bed Assisted Living. The servers were staff members. The aides primarily. They got the residents seated. The drinks and meals were served by the aides and the clean up done by the aides.

Yes, I would call the Corporate Office.

Are there microwaves in the rooms? They had them in Moms. If not, buy a small one for reheating.

My argument would be if there are enough people to deliver meals to residents then there should be enough to serve them in a single location. The serving on 100 (example) meals in a dining room would be faster than delivering 100 meals to individual rooms.
Staff shortage might not be just the people that serve but the kitchen staff as well.
The key here would be that residents can or should not complain of the meal served in the dining room is not as fast or as efficient as it was 18 - 24 months ago.
Keep in mind it has been difficult to find restaurant staff both front of the house and back. Traditionally waitstaff have been paid below minimum wage and TIPs are supposed to make up the rest. With shutdown both in facilities and restaurants and people ordering on line drivers like your Uber Eats driver can make $1000 a week and more depending on what they want to do. So with places opening up again it is getting difficult to lure these workers back.

Complain to corporate. They are going to have to become less greedy and pay staff better.

I agree with Cwillie, that they just don't want to pay a higher wage. My MIL's very well-run facility recently (this month) sent us out a letter stating what they were doing to solve their worker shortage and gave us a lot of detail about how they are giving bonuses to current staff, hiring bonuses to attract new people and an increase in wages overall. They have to do it, there's no other option right now. So you must complain, and loudly.

Why on earth wouldn't you complain to corporate, you are paying a hefty price for services that are not being delivered. The inability to find staff is a problem that is only going to get worse unless facilities are willing to bump wages (lol). And I honestly can't see the logic in this choice, seems to me it would take less people to serve the dining room than to deliver to each room.