Should I put this plant in soil?

I bought this plant a few months ago at a pet store. I have no idea what type is, but I refill the water anytime it gets low.

The leaves are starting to yellow a little bit and that has me wondering… Is it time to put this guy in soil? Has it outgrown this bowl?

I’d hate to shock it, but I’d love to see it get big and lush. Not sure what’s best and I’d love to learn from the best. Any tips appreciated!