Ubuntu – Ubuntu-software vs software-center

Like @dobey said, you should give the command sudo apt-get update a whirl. You may have a problem with your apt-cache and as such, you will have problems installing things.

Run the command sudo apt-get update && sudo apt-get upgrade. This will check for any and all updates/upgrades, hopefully fixing your system.

Once this runs, try running @sebastian_k's answer, sudo apt-get install software-center*. This will get/install anything and everything that Ubuntu Software Center needs to run.

Same thing happened to my ubuntu 20.04. The software center just went missing and along came out snap store. When I opened snap store, it is very similar with software center and it is doing the same job well. I think it snap store is now the de facto replacement for software center.