Fwiw, I keep 3 of my 4 bettas in 2.5 G tanks, the 4th one has a 5G. They have many plants, Hygro difformis, anubias, a tiny bit of java or bolbitis fern, a lot of moss, mostly java, but some others too, and a few frogbits. Each tank has an 8 inch round lamp on it, with a spiral 6500 K bulb, sitting right on top, or clamped within an inch or two of the top. I also have translucent mesh covers on the tanks, as I've had Bettas jump.
I do not do water changes often and I do not have filters or heaters, though if it's a very cold winter I might have to think about adding some heat.. I'll find out I guess. They changed the heating system here, up to now, it's always been too hot, most often I've had to run fans to keep it cool enough.
The plants consume all the ammonia and whatnot. All the plants came from cycled tanks, and while I did not cycle the Betta tanks, regular testing has shown me the plants and BB that are in these tanks are all that's needed to keep the water parameters in good shape. Testing always shows 0 ammonia, 0 nitrite and between 0 and <10 nitrates.
I found this surprising, but it works very well. I top up for evaporation, and about every 8 weeks, I do change most of the water, in the process of sucking up all the crud off the bottom of the tanks. They are bare bottoms, though I do keep a few oak leaves and an almond leaf in each tank, replacing them only when they are reduced to threads. There are few snails in the tanks too, but I remove any nuisance ones I find whenever I find them. I prefer to use Nerites in their tanks, but the 5G is also a temporary home to a bunch of Giant Ramshorn snails, and so far, the fish has not bothered them or their antennae. I keep an eye out to see he doesn't nibble them and so far, so good.
Some of the plants have a small snippet of a plant weight on them to prevent them all from floating, as there's no substrate.. just makes it easier to clean up. I also worry about a Betta's fins being abraded on some substrates, as I've seen this happen. It needs to be smooth and soft if you do have substrate.
I feed mostly live food, some frozen. The majority of the live stuff is aquatic and thus does not die if the fish takes some time to find and eat it. Of the 4 fish, two do not like man made food at all. One only eats if he's literally starving and even then, not much. He wants blackworms, and will also take fly larvae, flies and I'm hoping he's going to like scuds too. The other picky guy loves scuds and hunts them avidly, preferring them to black worms. I haven't had him very long, so hopefully he likes other things too. Given his hunting habit, I call him Scud, and he's got the 5G tank. It was my QT, will be again once I get another small tank for him and for the Giant Ramshorns. They appear to like it in there, they've laid more eggs in it.
I would disagree that Bettas are active fish too. They can be, but for the most part they don't move a lot. They're very good at energy conservation, and while I don't doubt some of them are more active than others, of my four, all spend most of their time just hanging around, except at feeding time. Even then, it takes them a minute or so to recognize food's being served and come to get it. Scud hasn't learned this at all yet, he ignores everything until he's hungry and then goes looking for it on the bottom. Weird.. but every fish is an individual.