If you are suggesting that a 10L tank is too small, why are the fighting fish always in tiny little glass tanks at pet shops?
Because the bettas are intended to be sold and not kept in those holding tanks permanently. Also, many pet stores simply don't give a toss about what they are selling as long as they make money from it.
Also why do pet stores keep their fighting fish in cold water when, in fact, they are tropical?
Because much like above, many basically either don't care or don't know. A lot of stores employ young people who have limited to no experience of the fish they are selling. That can also apply to many store owners. Just because they work in or own a fish store does not nessecarily mean they know or care. It is a business after all.
10l is
horrifically small, please for the love of god
don't keep him in that as a permanent home.
You can get a much bigger tank for very little money indeed. The largest size plastic critter Keeper is better than nothing and they don't cost too much either. Ebay is a great place for cheap second hand tanks.
A
5 gallon is the safest and easiest minimum size tank. That is NOT a large tank, it is not luxury or in any way extravagant , and will
easily fit on top of a strong/sturdy desk, table, sideboard or unit or chest of drawers ect.
( around 25-30 l 12x12x10 inches, or a tall hex tank ect - there is an aquarium calculator on this site, check the measurements of any tanks you see against this to find out the gallons )
Many places/people will tell you that bettas do not need a filter because they can breathe air. NOT TRUE. Their ability to take air from the surface does not make them immune to being poisoned by their own waste, or by waste food ect ( good job for removing it this is the right thing to do )
They are basically no different to Gouramis with regards to basic care. They DO need a nice gentle filter. A sponge filter is a safe and simple type, or a small Hang on the back type.
They also require a heater. They come from a very warm part of the world . 26-28 degrees C. I keep mine bang in the middle at 27 degrees C
25-50% water changes once a week and you're good to go.
A basic 5 gallon setup using a second hand tank or BIG plastic critter keeper ( I do mean the largest size not the standard) a heater and small basic filter with LOTS of silk plants ( never plastic it can cut their fins ) and plain basic gravel or aquarium sand should not cost too much at all and will be a LOT better for your fishes health, Plus easier fr you to keep stable and clean for him. with heated and clean water he should begin to feel much happier and also start eating too.