Ordered a spare set of wheels/tires for riding off road 4 months ago. They came in last week and I went for a ride this weekend.

What a difference!

Ran pressure at 45 PSI and the ride was quite comfortable. Felt no discomfort during the ride despite riding off road.

Is it possible to run street friendlier tires on tubeless?

Was going to order a carbon road bike but they're backed up too many months.

If you check manufacturer's websites, many tires are specified as "tubeless ready" or "tubeless compatible" or something. Sometimes it's in marketing cant, for example one of the things Schwalbe calls it is "TLE" (short for "Tubeless Easy").

There are plenty of road, city, and commuter tires that are tubeless ready.

When tubeless started, there weren't any tubeless specific tires. You can run basically any tire tubeless. One thing that can happen is that sometimes on tires that aren't designed with tubeless in mind is that the sidewalls can be porous enough that air will leak out. If you keep filling them with air, eventually the tubeless sealant will seal the sidewalls, but it can take a while.

I guess you could also have trouble with beads unseating if they were really loose or something, but I haven't actually heard of any problems with that.

With all that said, I don't know that there's a big benefit for street tires. The biggest benefits for mountain biking are that you can run lower pressures (better grip) without being subject to pinch flats (where you hit a bump and the pressure of the tire getting squished against the rim punches holes in the tube) and small punctures don't give you flats. Those things just haven't been problems for me riding on the street.