It's already clear from your first video what issue you're pointing out.
When you export from Photoshop, you're applying a different color profile.
The layers in the PSD file are stored as sRGB, but during export, Photoshop modifies those colors according to the selected profile — in your case, Display P3.
Spine doesn't apply any color profile. It simply reads the raw raster data and exports PNGs as-is (in sRGB).
If you want to export your PNGs with a specific color profile, you can try using the Photoshop to Spine script. Since it exports directly through Photoshop, the color profile should be preserved.
