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In my walstad tank I have some decaying plant matter as fertilizer. Now it looks like dirt at the bottom of a river. I have noticed my corydoras enjoy digging in this gunk, and my spotted cory will create a cloud of muck by waving his tail if scared, so he can swim away without being seen. I realized that this may be similar to their natural habitat. Has anyone else noticed this?

Just my opinion, but the soil under sand Walstad style is only practical in aquariums lacking any burrowing or digging species.
It is more of an interesting experiment to try but by and large is not well suited for the majority of aquarists. As I say, it is a style which may be fun to try but the vast majority of those who try do not become converts.

I think it is impractical to create a self-sustaining ecosystem in closed aquatic systems.
Keeping fish in aquariums is so artificial that it is the reason why so much has been invested in designing power filters, intense lighting and regular water changes. In short, it requires much input of energy to create a stable display aquarium meant to support a larger number of fish per cubic unit of measurement over long periods of time.
I believe Ms. Walstad herself recommends very low stocking levels for these kinds of tanks.

I would propose a hybrid where your major rooted plants are potted in soil covered with sand as one's first steps before attempting to duplicate her "natural style" of aquarium set ups.

Considering the species of fish most people want to keep like Corydoras and many plecos, sooner or later they will disrupt the underlying soil layer and then you can end up with a tank full of silty, muddy water.

I totally understand the appeal of a "natural" style tank but it does have the same intrinsic flaws as the biosphere experiments where miniaturized climatic zones, seas, lakes and jungles never worked out. The soil bacteria consumed more oxygen decaying organic matter than the plants could assimilate and the plants could not produce enough oxygen to make up for that loss and enough left over to support the humans and other animals they kept. Eventually the experimenters figured this out and continued to run the experiment but they had to have an external supplemental source of O2.

I have tried something similar in a 5 gal glass water bottle. I did not use any soil but I did use fine sand, tediously planted rooted plants and stocked it with 6 White Cloud Minnows. Everything had to be done with pronged sticks such as planting the rooted plants and I placed it near a window for lighting. I was able to keep it running this way for a couple years. I did make small, partial water changes but the White Clouds eventually died of old age. I replaced them with 6 Gold Medakas(Oryzias latipes) and kept it running another couple years so total time before I took it down was about 4 years. It was a fun and novel experience but I could not see it as a viable approach for a more normal aquarium where more fish and greater diversity is desired. It was my little world of fish in a bottle. I am glad I tried and I had no other particularly better use for the 5 gal jug so what the heck, why not give it a try. I did this over 35 years ago. If I were to try it again I might have gone with a few Cherry Shrimp in addition to the few fish. I used Corkscrew Vallisneria and some Tropical Hornwort for my plants. The Vals spread across the bottom and I periodically thinned excess growth from the Hornwort.

By and large, keeping soil under the sand makes a tank harder to keep than a more conventional approach.

So far the corydoras haven't disturbed the soil layer. I have a sand cap of 1.50 inches, all the way to 2.50 inches in the sandiest parts. All my fish seem much happier, and the plants are growing out of control. My corydoras do occasionally burrow, but they have never disturbed the soil. What I was talking about was soil like matter from decaying plants. My water params. are good and I do have a filter, not just plants.

Sounds like you have set up your "Walstad style" tank well.
There will be some composting going on in the soil layer but if you are good about making partial water changes, perhaps 50% each week, you shouldn't have any problems.
Eventually the soil layer will become exhausted of nutrients used by your plants and supplementary fertilization will become necessary but that may take a year or so before it becomes an issue. In principal, it is no different from any organic gardening where one uses compost. It's just that you can not easily supplement the compost in your tank and you may have to resort to an aquarium plant fertilizers eventually.

I have set up planted tanks using Florabase instead of soil and with supplemental substrate fertilizer the plants grow very well. I still use this approach in all my potted plants because most of my tanks only have about 1/4 inch layer of FloraBase bottom cover because I generally do not like bare bottom aquariums. FloraBase is expensive($20/12# bag) so it is expensive to use it as my sole substrate. I have done so, though, and my Echinodoras spp(Amazon Swords) send roots out so far they penetrate every bit of the substrate. I pot my plants because I move them around when I tire of a particular layout. Potted plants may be moved without damaging the root systems and causing shock to the plants. I often use the bottoms of clear plastic 2 liter juice bottles cut to be about 3-1/2 inches tall. These I can usually bury in the cheaper substrates to conceal the clear pots the plants are in. I use this method only for my major show plants and plant lessor species directly in the surrounding substrate whenever I use them.
I really like FloraBase because plants do extremely well in it, it doesn't alter water chemistry and it doesn't cloud the water if I have to disturb it. Despite it's high cost, it is what I use as the sole substrate in planted aquariums which are meant to remain set up for a long time. I could cover it with other substrates for special effects but it is so expensive, I generally avoid mixing it with other materials as I may want to reuse it.
It has all the qualities one might wish from soil but without so many unknown variables.

My experience is that a walstad aquarium is indistinguishable from a normal aquarium that's been running for a year or so; you just get to that point quicker.

As for the Corydoras... yes, they love digging in the mulm. I have seen the tail-flicking "sediment cloud" behavior you speak of in many different species of fish, but I have never reflected that it might not be just accidental from the rapid acceleration. However it does make sense for the fish to stir up sediment to hide the escape, so in retrospect it would almost be surprising if it's not intentional.