I thought I could distinguish a clicher 700c wheel from a tubular, but I'm not completely sure here. I think I see underlying tape and the tire does not easily come off, but I'm not 100% sure. I've attached pictures. The wheels are FiR, with 700x 20 Continental tires.

It's easier with the tire off. Used tubular rims will show evidence of glue or tape vs. rim tape, and tub rims will pretty clearly show themselves unable to hold onto a tire bead.

Well, there's part of the problem. I tried to get these tires off and couldn't.

Rims for tubular tires don't have raised sidewalls to hold the tire:

So what model of tire is it?

I can make out that it's a Continental. And I see what looks like a tire part number of 028636 along with the Bar and PSI pressures. So if with the left side of the tire being in such readable shape then what is on the right side of the tire. Which is usually for certain where they put the model and brand as properly bicycles are supposed to be photographed from the drive side or right side.

Looks like the brake track might be about to be worn out on that rim.

Deflate the tire and try to roll it off the rim. If it's a tubular tire, you will see the base tape:

If it's a clincher tire, you will see the raised sidewalls of the rim and the bead on the tire.

Thanks for the replies. It turned out to be a clincher. It was just stuck on weirdly.

Can this be rehabilitated by sanding?

The rim has some brand and/or model decals in it. Perhaps you could have googled that first. Andy

I did. It wasn't conclusive.

This can't be serious, can it?

The give away was the nut on the valve stem.

I recognize that the original question may have seemed a little silly for the experts, but the tire really was stuck on in a way that seemed like the whole thing was glued to the rim. It was like nothing I had ever experienced before. It gave way and opened about an hour later, but there was no way to get a tire lever in at first. The whole thing was monolithic. After I got the tire off, I saw that it was the liner that was causing the trouble. It's some kind of plastic that I guess got sticky and was acting like glue, holding everything together.

No amount of sanding will make the rim wall thicker.

The problem is not the brake track itself, but the structural integrity of the rim. Eventually, braking causes the walls of the rim to get so thin that tire pressure cracks them.

I see. Thanks.
Is there a rule of thumb for replacement?

If your thumb fits deeply in the groove left by the brake pads, replace the rim.

I would say when the rim wall is half its original depth thickness, but that may not be conservative enough.

These types of questions, "how much/little is enough" will never have an answer that pertains to every rider. As a rim brake track wears and gets thinner it will begin to flex outwards more until the cracks start. How sensitive to brake feel is the rider and will they feel this widening as a late term heads up? What pressures does the rider run, more PSI is greater side wall widening stress. How abrasive are the pads? How much grit and such are carried up and onto the rims during riding? How much braking force is used during one's rides? How tolerant of a rim's brake track blow out is the rider? Will they sue someone or just accept it as what pushing limits can get you?

Some rim brands do have wear indicators and guidelines for rim wear. I assume the "spec" is somewhat liability driven... Andy

I took the wheels to my LBS. I was potentially interested in new rims and having them build me new wheels. They said what I have are fine...happy even to see a FiR rims in the flesh. Good shop.

Be very gentle with sanding or filing any really high or rough spots.

I've only had one rim fail years ago. The brake tracks were worn very concave, until one day the lip of the rim just popped off.

I can see a couple of worn spots on your rim, but it is difficult to discern how bad it is overall.

The appearance of the sidewalls make the tires seem to be shot anyway. In such cases, where the tires are hard to come off, I just cut through the tire and peel it off like a banana skin.

I had a pair of Shimano Ultegra wheels purchased in 2004. The hubs ran smoothly with no play. I checked the trueness occasionally, but they needed minimum adjustment.
In 2020 the rear wheel's braking surface showed a minor vertical crack so I decided to measure the thickness of the braking surface with a special tool.
I found that both sides on the braking surface of the rear wheel measured 0.7 to 0.9 mm. The front wheel was slightly better. Most of my riding is done in dry conditions.
I decided to replace these wheels.