What does a belly button Z-Plasty look like?

You did not post any photos, so I cannot be specific. The Z-plasty heals in the shape of the Z and helps lengthen the compressed area.

A Z-plasty is a procedure that lengthens tissue in one direction by recruiting tissue from the perpendicular direction. It also breaks up the linear direction of a scar.
If the surgeon could not adequately describe the procedure or show you before and after pictures then maybe you haven’t found the right provider.
Umbilical revisions are hard and often don’t lead to much improvement. It depends on “what the problem” is. Consider including pictures. Attempts at making a new belly button are often not views as successful or great.
Unless surgery is going to help you it may be better to wait or not have a revision.
We need a bit more info to give you a good recommendation
Mats Hagström MD