Relisten to the Sonnenburgs rather limited endorsement of prebiotics/fermented foods, primarily as temporary "placeholders" that can deter pathogens in immediate aftermath of a course of antibiotics.
The microbial species that predominate in kimchi, sauerkraut and other fermented foods are very minor constituents of the gut microbiome. Fermented food advocates don't have much support in the literature for lasting positive effects on the colonic microbiota. I found a couple studies where bacterial RNA from fermented foods could be detected in feces, but as with probiotics, they don't compete effectively with established populations and disappear after the interventions.
The greatest effect of fermented foods may in fact be antimicrobial, as bacteria and yeast compete in a state of constant chemical warfare, producing bacteriocins and nisins, often targeting closely related strains. Eg Kimchi: 1, 2, 3, 4; kombucha: 5, 6; sauerkraut: 7; tempeh: 8
Little of the antimicrobial proteins from fermenters would make their way to the colon, so I'd mostly expect a benefit to dental health.
Among the species that both comprise a large fraction of healthy colon microbiota and are generally considered beneficial, only *Bifidobacterium longum* is available as a probiotic. Others, like Akkermansia mucinophila, Faecalbacterium prauznitzi, and Roseburia, are introduced with general exposure to a non-sterile environment, and avoidance of unnecessary antibiotics. One feeds them with microbiota available carbohydrates, mostly from beans, bulbs, and bran.
• galactans: beans, though little in green beans, tofu or tempeh.
• fructans: white parts of all Allium bulb vegetables (garlic, leeks, onion, shallot, scallion), particularly raw or lightly cooked, some crucifers (broccoli, Brussels sprouts, cabbage), raddichio, snow peas, modest amounts in asparagus, peppers, beets, and okra
• inulin (a longer chain fructan): chicory, jerusalem and globe artichokes
• arabinoxylans: wheat, barley, and rye bran, and grain products made with these
• resistant starch: a high fraction of some raw starches (potato starch or green banana), moderate amounts in some unleavened flatbreads (eg, maize tortillas), as well as starches that have undergone retrogradation (eg, cooked then slowly cooled potatoes, pasta and porridges).
Bringing the discussion back to the topic of dietary protein, here's a very intriguing study which found excess protein intake could shift the colonic microbiota towards a community with potentially pathogenic species that rely on exogenous dietary protein, and away from a more beneficial community that relies on host-provided mucin production (eg centered on Akkermansia). Unfortunately, the graphical abstract is a lot clearer than most of its verbiage.
Holmes et al., 2017. Diet-microbiome interactions in health are controlled by intestinal nitrogen source constraints. Cell metabolism, 25(1), pp.140-151.