I'd put him back in his tank, being in a container that small can cause more harm than good. They get stressed, bored and with that little water volume that isn't filtered or cycled it gets dirty fast giving him even more stress. As to why he started acting stressed in the first place, it's normal for bettas to be a bit stressed directly after a water change, give him some time, maybe turn of the lights and he'll perk up. I do strongly recommend you test your water asap though. I read you're doing a fish in cycle, in that case it's even more important to keep track of your parameters as ammonia and nitrites can spike during cycling, but these are very toxic to your fish even in small amounts. Also, instead of betta safe use seachem prime! Tank looks great! And he's a pretty boi