A chromotherapy sauna is a cabin with colored LED lighting you can change, usually offered as a paid option on infrared models. The lighting is pleasant and the naming is a health claim, and those two facts should be separated before you decide whether the option is worth its price.
What you actually get
A set of colored LEDs, a controller and usually a cycling mode, mounted in the cabin ceiling or a corner. Physically it is mood lighting rated for the heat. Some cabins include it, some charge a few hundred dollars for it, and a few reserve it for the higher models as a way of differentiating them.
What chromotherapy claims
Color therapy claims that specific colors produce specific physiological or psychological effects: blue calming, red energising and so on. There is no competent and reliable body of evidence supporting those specific claims for colored light in a sauna. Light does affect mood and circadian rhythm, which is not the same thing and does not validate the framing.
Is it worth paying for
As mood lighting, if you like it and the price is modest, sure: a cabin you enjoy being in is a cabin you use. As a health feature, no, and a maker charging a large premium for it on that basis is selling you something they cannot support. Judge it exactly as you would judge colored lighting in any other room.
Red light is a separate question
Do not confuse a chromotherapy LED with a red light therapy panel. Therapy panels are specified by wavelength and irradiance at a stated distance; a chromotherapy LED is a decorative color with neither figure published. If red light therapy is what you want, that is a different product with different specifications to read.
Questions people ask about chromotherapy sauna
Does chromotherapy do anything?
As lighting, it changes how the cabin feels. The specific health claims made for color therapy are not supported by competent evidence.
Is it the same as red light therapy?
No. A therapy panel is specified by wavelength and irradiance at a distance. A chromotherapy LED publishes neither.
Should I pay extra for it?
Only as mood lighting you will enjoy, and only if the premium is small. Not as a health feature.