You can safely put it in a pot now but I would provide it some humidity cover until it roots in enough to remove the humidity "cover". Do NOT over water it though.

Maybe put a loose plastic bag over it for a week or so, like a clear produce bag. keep it where it is unless it was getting any direct sun

This is wild seeing a rhizome in water! I've rooted many individual leaves this way, but never any rhizome. I'm surprised it did not rot. Very interesting experiment. It looks like it will be awkward to put the rhizome on the soil surface, but if any of the leaves are going in the wrong direction, you can snap them off to propagate.

A rhizome is like a cane - just shorter internodes and a thicker stem so water rooting should work as well for a rhizome as a cane. I wouldn't do it that way but as we can plainly see, it does indeed work.

Thanks, everyone! This was gifted to me by my MIL, from her mother plant, and this is how she has always rooted her cuttings. I didn't know there was another way until now - so interesting! I am ready to put it into a pot but she is suggesting the roots get a little stronger/hardier - so I will wait another couple weeks. I will definitely use the humidity cover and be mindful of how much water I give her. Appreciate all the feedback!