Lethargic Betta or Fish with Personality?

I recently bought a male half-moon betta from my local PetSmart. I have owned 2 other betta fish in my lifetime, as well as African Aquatic Dwarf Frogs.

This betta, (named Pluto) has been fine the first two days but now shows a large interest in hiding/sleeping. He comes up for air and every once and a while he'll swim around, but his swimming pattern is in bolts, as if nervous. Pluto seems to be eating fine, I'm trying not to overfeed him. I've been spoiling him and have played prolonged aquarium videos from my laptop near his tank.
His sleeping habit in the log decor has also got me concerned, because oftentimes I notice he's laying on his side whenever I look inside the log, but will always perk up and start swimming again if I turn my lamp off and on to make sure he's okay.

My tank is a filtered 1 gallon. Within the hour I put a heater in his tank to see if that would help. The heater isn't necessary in this season but when the weather cools down I would for sure use it, which is why I'm hesitant on keeping it in there, because it doesn't have a temperature gauge and I'm afraid of overheating. In the tank I also have a live marimo and a decorative log to serve as his hiding place.

I usually do 100% water changes once a week (my tank is filtered). Today I used a plastic water bottle to make a "bufferer" to keep the current from being as strong.

Usually bettas are active and curious, but Pluto seems tired and stressed. Maybe it's just behavior? I don't notice anything physically wrong with him, and I've researched common signs of illness but still can't find out if anything's wrong.