Some astro photographers use StarNet[1] to remove stars altogether. This allows you to blend them back in[2], potentially after additional processing.
As the name suggests, StarNet uses neural network for the job[3], and at least yet hasn't been trained on Webb data AFAIK, so might not do a good job there.
There also seems to be a similar tool with the same name over on github[4], but seems to be a separate effort.
[1]: https://www.starnetastro.com/
[2]: https://astrobackyard.com/starnet-astrophotography/