Seems like it would be a function of telescope type, rather than raw aperture. Like an entirely apo all-reflective telescope. That is, if you are only interested that one star, and not e.g. the entire constellation... then you would need no significant field and not even resolution (given that any star is an unresolved point source to amateurs). Just put your camera on a Newtonian telescope and collect an exposure series to get the color of the star. Also worth trying intentional defocus, so that the (doughnut) of light will integrate the color over hundreds of pixels, unsaturated. Then you could analyze the color quite accurately, e.g. x,y,z chromaticity or even a bunch of bandpass filters for extended color NIR, R, G, B, NUV. The epitome of spectral analysis would, of course, be --- a spectroscope, with the star on the slit! And that should sure be interesting... to look for changes in the spectrum as it wanes and waxes. Obviously, the professionals are doing that sorta stuff right now, and we amateurs who are into spectroscopy could also enjoy the ride. Thankfully, Betelgeuse is bright enough to do stellar spectroscopy with a modest amateur telescope!
I think that answers what you are getting at? Tom