Sorry my pictures are not great but tail looks odd shape. Could this be if it has been nipped
Yes, could well be damage from another fish, which then allow secondary infections like fungal and bacterial infections to set in. Were both those photos taken on the same day? Because it looks worse in the second one.
Some tetra and barbs can be nippy too, going after other fish, especially if they don't have enough of their own species to keep them occupied and less stressed. However, the tetra you have are generally peaceful even if you only have a few of them, and you weren't experiencing this until the betta was added, so I'm sorry, beautiful betta, but knowing how bettas can be if they decide the whole tank i their territory, they will absolutely bully, injure and sometime kill other fish in the tank.
If you go to the search function, type "betta killed my" into the keywords part (include quotation marks) and search threads, you'll see example after example of bettas in community tanks killing other fish. These are the results!
www.fishforums.net
They're not nasty fish at all. Just solitary and territorial, and doing exactly what they'd do in the wild to protect their bubble nests and fry (for males) and because once female bettas mature, they are also solitary and travel around, searching for males to spawn with. They don't live in one area with other fish, and also have that drive to chase other fish away and don't desire company the way shoaling species like tetra and corydoras do.
In the wild when a female finds a male and they both want to spawn, they'll mate, release eggs, often both collect them and place them in the bubble nest. But then the female will leave, and the male will fiercely guard the nest, the fry, and his territory. He'll chase off the female if she lingers for too long. Problem in our tanks is that the female can't just go her own way. So betta breeders are very aware of this, carefully introduce the fish and supervise, then get the female out of there when they're done, because he can easily kill her since she can't leave his territory and the bubble nest.
A "one-night stand" kind of fish
Don't form long term bonds and remain together like some species, say a pair of angelfish do.
But it works for them and their natural environment! They're labyrinth fish and can survive in conditions we'd never imagine. Fascinating fish, and personable in the way you can hand feed and interact with them.
Personally I'd recommend clearing a spot, searching on places like Gumtree and FB marketplace for a 5-10 US gallon (22 litres - 45 litres for us metric countries!) second hand tank that comes with equipment like filter, lights, heater. Lots of them available for cheap where people have tried and given up, or upgraded tanks and don't want the previous kit anymore. I wouldn't keep a betta in anything less than 5 US gallons/22L, and ideally larger. A 10g/45L is pretty idea, and can make a lovely little home for her!
I just bought a decent second hand little 7g tank on Gumtree for £20, and includes everything she wanted rid of, lol! So four small filters, airpump and ornaments that you can use as bubblers & decor, suitably sized heater, lights etc. A bargain, just needs a good clean, and at the moment I'm planning to pop it on the kitchen counter. Cleared a nice spot for him! (he's in a QT tank right now since I only got my betta end of July).
I haven't tested his temperament with things like shrimp or snails yet, but have to say, I'm used to feeding community tanks, even when I'm targeting certain foods for certain species. But having a single fish in a tank to feed - who comes to me for feeding whenever I'm near the tank (I have to tell him it's not dinner time everytime!) feels different, and I'm enjoying it.
And I'm someone who swore I'd never get a betta! Haha. Love him. Excited about the tank set up I'm making for him! This 12.5g tank he's in now is my old QT/grow out/nursery tank for guppy and cory fry. It's useful for those things, but light is so weak that no live plants last in it for long, even through they thrive in my other tanks:
I saw a cryptocoryne and perhaps an amazon sword in your tank? You said they turned to mush, I suspect you went through what's called "crypt melt". Nothing you did wrong, and if you'd left the roots in the tank, the crypt would likely have regrown. Can google "crypt melt" for more info, and how aquarium plants need to adjust when moved and replanted into a new tank, especially if they were grown out of water, and then have to convert to their underwater forms. Amazon swords commonly go through this, and the old leaves begin to die off, looks rough for a while, but with some light and nutrients, they're usually growing new, submerged and healthy leaves, and just don't need the old leaves anymore. It's not that the plant is dead or dying. Think of it like trees shedding leaves in Autumn and looking bare, until they burst out fresh new growth in Spring!
Crypt melt convinces a lot of people the plants are dead and they failed, but isn't something you did wrong. Just plants don't naturally move around in nature
So being replanted, repotted, unpotted and planted into substrate means the plant needs time to settle in and get itself established, put out new growth again.
Lots of patience with planted tanks, and it's a learning curve! Just have to remember that plants take time to establish their roots and out out new growth, and will sometimes melt back but recover, or look a bit rough for a while as they adjust to their environment.
Last example - I set up this tank with plants and fish I bought at a local fish club event (much cheaper than stores, chance to meet other hobbyists, and healthy, beautiful, locally bred fish! Recommending finding fish clubs and events in your local area. I joined FB and BAND apps to find other local hobbyists and clubs, and we sometimes trade fish and plants too.
)
Anyhow, I'd just left the plants floating in the QT after I bought then July 28th. But then moved the tank and set it up more like a proper tank, planting the plants and deeper substrate. Used Argos play sand - it's aquarium safe, super cheap, so don't mind if I have to chuck it from a QT tank if a disease or problem did crop up. I already had the wood and stone hardscape, and the plants are trimmings and new plants grown by other hobbyists and sold super cheap. I got three of them, the vallis, guppy grass and another for £2!
Tank set up and plants actually planted 3rd August. Looked like this day one:
Then like this by the 16th! Tons of new growth. I didn't even really notice just how much until I took the photos and compared them.
Haven't used any ferts yet, no CO2, light is a cheap Nicrew light, but it's good enough since I've used Nicrew lights for all the tanks in the photos above. So I reckon when it comes to plants, a more LED light strip might help, but you possibly also just had crypt melt or plants struggling to convert to submersed form. You too can do this! The fish love it, and it helps so much with water quality, since plants suck up the ammonia fish produce and use it to grow, and they can do it a lot faster than the nitrifying bacteria.
We'd be happy to help you with stocking suggestions since you'd like new fish! Or plant tips, anything really! We're generally a friendly bunch