Inevitably, star removal needs something like Photoshop. A popular diy method is to remove stars by selecting a colour. I haven't ever tried it but you could use it to select say blue stars and redder ones separately. This would work I expect using GIMP, the freeware PS equivalent.
This won't give you the stars as a separate layer. This is useful to have. You can remove the stars and process the object and background without affecting star colours or increasing their size. This can happen with stretching if highlights are brought out. The star layer can also be processed on its own, eg saturation to bring out colour, and then be recombined with the starless layer.
Making star layers in photoshop requires use of masks. I have come across youtube videos that will walk you through it. Maybe GIMP could do this too.
On the other hand, even good cooks buy ready made puff pastry rather than make it themselves. Guaranteed to rise! The proprietary softwares can be quite expensive but I find PS action sets work very well and can be excellent value for money. In particular, Annie's Actions, at a cost of $20, does star removal and star layer, and they include a wide range of other useful enhancements and automated image RGB and narrowband composition. You do of course need Photoshop, though the elderly open access CS2 version may be still available and in my experience does most things that later versions do, if not so conveniently. It needs a key to activate but that is also on line with a bit of determined searching.
Annie's actions also seem to cope well with evolving hardware, unlike say the Carboni Actions and Gradient Xterminator which require a new full price purchase if you move from 32 to 64 bit computer processors.
A layered gif is a great idea, showing with and without stars and perhaps the ability to reduce progressively the number of stars in the star layer to taste. Beyond me though.