Why is my wheel going out of true after I mount and inflate the tire? I’m wrapping up my very first wheel build (rear wheel), and I noticed that the wheel is going out of true after I installed the tire. Before installing the tire, I had the wheel trued pretty well (within one millimeter in all directions). With the tire on, it’s now got a few millimeters of lateral runout. What could be causing this?
The rim is a 29” 28h Stans Arch MK3. The spokes and hub are generic, although I will mention that the spokes are significantly too short. I am replacing the rim, which cracked after a period of riding MTB with chronically low tire pressure (and thus many rim strikes.) The new rim is shallower than the old one, so the ERD is bigger. The tires are set up tubeless. I don’t presently have a tension meter, but I can tell you that the spoke tension is pretty even (squeeze method) and is comparable to the other three wheels I own, maybe a bit lower. I don’t want to overdo the tension, especially on a MTB which will see jumps and drops. I will borrow my friend’s meter and update the question.
Side question: why are the spokes not equally screwed into the nipples? Of course, there might be discrepancy between the drive- and non-drive sides, but on the same side, there’s a millimeter or two of difference. The wheel is true (without a tire), so why is there a difference?
Update 1: Deflating the tire brings the wheel slightly back into true. Dismounting the beads brought it most of the way back, although it is still wigglier than I remember trueing it to. It’s only lateral true that is affected; radial has been pretty much perfect the whole time.

More photos without the cassette:
why are the spokes not equally screwed into the nipples? Of course, there might be discrepancy between the drive- and non-drive sides, but on the same side, there’s a millimeter or two of difference.

That's a sign spoke tensions are not equal.
The fact that spoke tensions are not equal is a sign spoke tensions are low.
Increase your spoke tensions to the required level and equalize them.
Besides, how did you see that spokes are not equally screwed? Do you see the threads below the spoke ends at the rim? If you do, the spokes are too short. The only way that in a well-built wheel you can observe if spokes are equally screwed is to look at the spoke threaded end inside the rim.

Before installing the tire, I had the wheel trued pretty well (within one millimeter in all directions). With the tire on, it’s now got a few millimeters of lateral runout. What could be causing this?

Tire inflation pressure affects spoke tension. The more inflation you have, the less spoke tension you have.
To ensure this is not a problem, the tension of spokes before inflation needs to be as high as possible.