Is the red ring surrounding Proxima in the top image an artifact of processing or a nebula surrounding the star?
There is no nebula surrounding Alpha Centauri. This a photographic effect, quite possibly enhanced by processing. You can see that the blue ring surrounding bright Beta Centauri is quite strong, too. That ring, or halo, correctly demonstrates that Beta Centauri is a hot blue early B-type star. The red color of the halo around Alpha Centauri suggests that it is a red giant or a red dwarf, which it certainly is not.
If you have ever observed a star through a telescope, you may have noticed that it may be easier to discern the color of a star if you unfocus the star a bit. Stars are brilliant point sources, so that they are usually overexposed in the middle. If the stars are very faint, their light may simply not be enough to stimulate color vision in our eyes. There is a "middle brightness level" where the light of the star is not overexposed but bright enough to make it possible for us to detect color.
In photography, this effect is even stronger. There is a photographic effect that I can't explain, though it may possibly be called unsharp masking, which works so that it creates colored haloes around brighter stars. This brings out the brighter stars and makes them very obvious compared with fainter stars. It also brings out the color of the stars. Therefore, the fact that Alpha Centauri is surrounded by a halo at all is a deliberate photographic technique.
Another way to bring out the colors of the stars is the step-focus technique. This image shows the Southern Cross is such a way that the stars become more and more unfocussed, step by step.
On the lower left in this picture, you can actually see Alpha Centauri. My impression of the color of it, as seen in this image, is that it appears to be bluish.
This photo was almost certainly taken by Akira Fuji. It shows the Southern Cross on the right and Alpha and Beta Centauri on the left. Alpha Centauri is marked with an arrow. You can see that Alpha Centauri appears to be colorless, or white, possibly with just a hint of yellow. This is the "true" color of Alpha Centauri, at least if you accept the idea that the Sun is white and compare the RGB color of other stars with the RGB color of the Sun.
The Marco Lorenzi picture of Alpha, Beta and Proxima Centauri is admirable and very, very good, but I would say that Lorenzi got the color of the halo around Alpha Centauri wrong for one reason or another. The color of Alpha Centauri is very close to the color of the Sun, although it is a little bit yellower. It certainly is neither red nor blue.
I would say, in closing, that getting a good RGB color balance "all over the face" of an RGB color picture is a very tricky business.
EDIT: Oh! I see now that you asked about the red ring around tiny Proxima
Centauri. Well, basically the same technique has been used here. The photo was taken is such a way that there are haloes around the stars. The haloes are small, however, because the stars are not very overexposed, and they all look pretty faint. Why is Proxima so red-looking? It is possible that Proxima is the reddest star in the field shown in that picture. I've tried to check that out with the help of my software, but unfortunately my software doesn't have a lot of information about 11th magnitude stars in general.
Apart from being cool and red (B-V index = 1.8), Proxima Centauri is exceedingly faint. We can be sure that all other stars seen in that field are intrinsically brighter than Proxima. (To the best of our knowledge, all
other stars that we can see in the sky are at least farther away than Proxima, although not all of them are intrinsically fainter.)
It is likely that most of the other stars in this field are not even M-type stars, because most M-type stars are puny little red dwarfs and very faint. So most stars seen in the picture with Proxima in the center are hotter than Proxima and therefore less red. But we can't be sure that this is true of all of them. There may be some distant, highly reddened and/or intrinsically very cool bright giant stars that are seen in this field, and they may well be redder or redder-looking than Proxima.
There are two possibilities. Either Proxima Centauri is indeed the reddest star in the field. Or else it is red enough, but not the reddest, and in that case some processing has been used to enhance the red color of Proxima.