Male betta always sleeping?

You can rearrange his decor, get him a tank mate, play with him more... But have you checked all his parameters? Has his heater crashed? Has the cycle had a hiccup?

We actually just did a full water change because there was a lot of algea. We got him new rocks and a new fake plant that he totally loves, and we bought him a new heater that keeps the temperature regulated (the one we had before didn't auto shut off so the temp fluctuated a lot). His water seems a little cloudy now and I'm not sure why (maybe everything is still settling?) But prior to the water change he was just sitting in his cave a lot too.

What tank mates are good? He doesn't seem very aggressive, he never flares when he sees his reflection or anything, he just kind of hangs out. Wasn't sure what I could put in there, but I was thinking that would at least give him something to play with since I'm at work all day and my daughter is at school.

I would get some shrimp or a snail, nothing larger. So he was lethargic before the wc? Did that perk him up?

It didn't seem to help. The new plant I got him is tall and he just lays on top of it near the top of the water all day, or he stays in his cage and pokes out his head to stare at us while we try to get him to come out and play. He comes right out when it's time for food in the morning, but that's about it. He does swim around sometimes, last night we had him going for about 5-10 minutes, but every time I go check on him he is either on top of the plant or in the cave.