In Blender and Unity, my model looks like this with a pixel template overlay:
Whereas in UB Painter, it looks like:
You can see the texture UV displays here (Blender) and here (UB Painter).
It isn't a major offset but it can definitely throw off some pixel painting, especially when you're trying to get clean lines in your textures at lower resolutions. I'm not sure if it's a Godot issue (it might be worth putting a bug report in to them if so?) or something UB Painter is doing. It looks like it's purely a rendering issue -- if I export the mesh back out of UB Painter into Unity, the UVs work fine.
I can send an obj file of the model and a pixel template texture if it would help diagnose the issue.