I feel like the stars are probably pretty easy to mask out since they’re very bright relative to the rest of the image. Once you have the mask, each one is small enough that you could probably fill it with the values from adjacent pixels. Kinda like sensor mapping to hide dead pixels. That’s just a guess though, I’m sure there’s more to it than that.
Bright stars are so bright they literally mask areas of the sky. You'll probably need deconvolution algorithms (CLEAN being the standard some time ago, don't know whether some AI/deep-inv approach works nowadays...) to remove them.
There are several “AI” deconvolution tools to remove stars which work exceptionally well: two of the most popular ones being StarNet and RC-Astro’s StarXTerminator. I’m willing to bet that the author used the latter for star removal as it’s become something of a standard in the astrophotography world.