Personally I stay keto/low carb but also look after my gut microbiome. I don’t think there’s an incompatibility especially as Dr Tim Spector lists things like a sprinkle of mixed herbs, spices, a few seeds and nuts and all vegetables (many of which happily fit in the low carb camp) - which all contribute to gut bacteria diversity. No minimum quantities are listed just the importance of a diversity. Live full fat yoghurt too fits well into keto/low carb. Fermented food such as kimchi and sauerkraut are often very low carb and help too. Issue often is what people believe a keto or low carb diet is whereas by personal choice it can very varied. I keep my diet as diverse as possible as it suits me and my gut and my bgs but don’t eat large quantities of veggies in total as not convinced by the eat a certain amount of fibre -gut bacteria need prebiotics for sure but a diversity even in small amounts is I believe the most important way to diversity your bacteria. I also make my own bio yoghurt- Check out Dr William Davis too and his yoghurt recipes.
Key message, from my understanding, is stay away from processed food, seed oils, sugars and wheat and grains and work out a diverse low carb way of eating that suits your own bgs and gut health and most importantly that you enjoy and stick with.hope you manage to work out a way of eating that suits you and your metabolic health.