I am sorry to hear that it was not resolved. I tried the Online Image Compressor you shared using the Spineboy's texture, and I could see the same artifacts in the outlines of some images. The compressor does not seem to have very fine quality settings, so it may be difficult to adjust it so that such artifacts do not occur with that. Here is the result when tested with Spineboy (Click to enlarge and you can easily see the difference) :
An alternative might be to use Spine 4.1 to compress the texture. The latest 4.1-beta has greatly enhanced the PNG export settings, allowing for size reduction while maintaining clean image quality. As a test, I created a Spine project with only the texture placed and compressed it as follows:
The result is here:
Texture size with no compression: 3.3MB
Texture size compressed using Spine 4.1.26-beta: 533KB
However, it will be tedious to do the export manually, so it is better to write a script and run it with CLI; if you run Spine via CLI, you can temporarily launch 4.1-beta and do the export without changing the editor version which you are using. This should be more efficient.
I just wanted to show one of the possibilities that might allow you to complete the whole process using only Spine, and I hope you understand in advance that it may not be a perfect method.
If there is anything that is unclear or you would like to ask additionally, please do not hesitate to let us know.