But the compressor never got shut off, and the AC is fully charged and
not subject to freezing, and most importantly I can run in any of
those 3 speeds for a long time and nothing changes.

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You really need to do a "performance test" which is basically open the doors, run on outside air and measure the incoming temp/humidity (Use weather bureau for humidity) and discharge temps.

You should get between 15 and 20 degree difference in temperature. A lower difference, if the humidity is high.

The compressor really should never shut off in a more modern vehicle unless the evaporator is in danger of freezing. Freezing is possible if your using the AC when it's 40 degrees outside, which I frequently do.