Moving Betta to new tank?

I bought a betta fish about 5 months ago. He is currently in a 3 gallon tank with a snail.

He seems happy and energetic. He has no problems eating his food, and he even makes bubble nests (which I heard is a good thing)

I want to move him to a bigger tank. Possibly a 20 Gallon.

Should I just leave him where he is since he’s happy, or move him to a bigger tank? I’m scared he may get stressed being moved.

And if I do move him to a bigger tank, are there any fish that betta can get along with?

Any help is appreciated!

Thanks!