I’m not sure what material or style these steps are, but they’ve started crumbling after water got into a crack and froze during the winter. It seems to be getting worse and I’m wondering how to address it. Is this something that can be patched or do I need to remove all this material and start over?
those steps were going to break at some point.
You can't simply mix up some cement and fix it. Cement doesn't glue to it'self after it's set up. You'll need a special mixture to get anything to stick to it reasonably well.
Plan on getting the steps redone, and patch it with some repair mix for the short term.