Glad to hear you've figured it out! Do you mean that the original file size is 4096 and it was set to Max Size 2048?
If so, then this would most likely be due to this known bug in Unity. The ticket says it's fixed in 2020.1 (in March last year I received a mail claiming it's fixed in 2020.2, so at least there it should be).

I thought the issue was coming from having inconsistent max size resolution (1 texture being repacked had a different max size than the others). But I tested again after reading your comment and you are right: using Quality Settings to lower the texture size is creating the bug, even if the max size are consistent. It's good to know it has been fixed in a later Unity version (We are using 2020.1.0f1 at the moment and in the bug post they are saying it's fixed in 2020.2.0a6).

Regarding the cropped images, do you receive half or quarter sections (in contrast to arbitrarily cropped sections)? If so, then this should be due to the above bug with half or quarter resolution texture settings (either in Quality Settings, then check out the active quality tier, or via max texture resolution). Could you please check these settings as well? If not, could you please post a screenshot showing the cropped image?

I used the same character and this time exported its texture with "rotation" enabled. Without using the repack, everything is working fine. Now using the repack, there is something I never saw... one texture element is combining the two issues: it is cropped and its also not appearing. The absolute dimension of the texture is 876x1027 and it's max size is set to 4096 (increasing it does not change anything). See screenshot below:

Thanks for following up Harald.

Is the region gray in the resulting packed texture? Could you please post a screenshot of the resulting packed texture as well as the source texture?

What is weird is that the face region is inside the texture and displayed properly, yet there is a a grey area somewhere else. Also, by looking at the texture, I noticed that many arms regions were weird. I tried displaying some and they are randomly cut too. But just by looking at the repacked texture as a whole one can see that something is odd.

Maybe the non-power-of-two is causing problems here, although the Texture Import settings look correct. Could you test what happens when you enable "Power of two" in the Spine export settings?

Ticking "power of 2" at export is solving the grey area issue and actually showing that the face region is duplicated on the texture. But as you can see there is still some random cuts. I checked my exported texture and the face region is not appearing twice there.

Ok, I'll try to do this next week. I keep you updated.

Thanks for investigating and helping us!

Awesome, thanks Harald!
I don't think I'll manage to try it out before next week. I keep you updated