Fiber feeds ALL of the microbiome. If you have a bacterial imbalance (i.e. IBS, SIBO), fiber can ferment and contribute to symptoms. It can be more broadly said that high(er) fiber diets benefit the normal microbiome in individuals with healthy intestines.
Lots of people are on a ZERO fiber diet - and they do fine! The thing is, our “microbiome” adjusts to what we eat. Or do not eat. One cannot define a “healthy microbiome” based on either the Standard American Diet OR Vegetarian diets.