A lot of people recommending to qt and some saying you can treat them in the main tank for the treatment. I think you can really do it in the main tank .Well you have a snail so you can't do it. Usually if you treating with aquarium salt you need to finish whole course of it 10-14 days. And answer to your question, if you should keep him qt for longer, you really don't have to. The people recommending it because of the frequency of the water changes and treatment. So if you can do it in the main tank you can put him there and do water changes in the main tank.
Any time when you have a divided tank with another betta then of course you need to qt sick betta right away and do not share anything between them. And even do a large water change in the main tank for prevention . With some disease ,its even helpless to qt them because the tank already contaminated and you have to treat whole tank. That is why i am super careful with my bettas and all have separate changing equipment for each of them. I am crazy about it. I don't know why i decided that your tank is divided with 2 bettas when you clearly saying that you have 2 tanks, sorry .
So you can transfer him back and do frequent water changes and see how he doing. And if you think he is getting worse especially if he has any behavior changes you can treat him with salt again and see if its helps. The minimum therapeutic dose of the aq salt though is 1 tsp/gall with daily water changes. The maximum dose is 3tsp/gall depends on severity. The instruction on the salt box is just for the preventative care.
How long you have them?
Forgive me Hallyx i know you like to cycle the tanks. But i don't like to cycle and use the filter for the 3 gall tanks. So i would always just recommend to do regular water changes. Because cycling can crashed easily in the smaller tanks and give you a problem.
But if you want to continue to have the filters in your 3 gall tanks i would do frequent water changes for now and see hoe both of them doing.
Recommendation for the water changes in the 3 gall tank with the filter is 2-50% water changes a week, with the gravel vacuuming , + make sure you swish /rinse the filter media in the tank water regularly as it can gather a lot of gunk on them and that could cause ammonia spike.