Yes. It seems to be connected with the synthesis of short-chain fatty acids by gut bacteria. Beta-glucan is also helpful in this regard; sources include porridge oats, mushrooms and supplementation.

Agreed. Specifically, prebiotic foods & foods that contain cultures (such as yogurt) make most sense to me (as a layperson).

Fermented foods like Sauerkraut as well

I’m not an expert but from what I’ve read you don’t need to eat the biota to get them, you just need to make them a happy home and they’ll find their way into your gut.

My sense is that's right, but it makes it sounds a little too magical. It might be better to say that most of the strains you want to encourage are already present, but a diet with lots of fiber (aka 'prebiotics') will encourage the good strains to outcompete the bad strains. It's a pretty complex balance, there are also phages, and some fungi all mixed up in there.

It was a long time ago now but I remember reading an article about a researcher who tested his gut biome every day or so and it was amazing how quickly things change depending on what you eat.