Think about how you'd do it as a human, that's usually the answer for these things in my experience.
If you've ever worked with any workflow engine, doing it with agents is largely the same. If you were writing some automation that used a browser, how would you handle recovery for any given step of your workflow? It depends on what you're doing, the specifics of the web app you're interfacing with, etc.
Contrived example, but let's say you're sending an email. Load the page, click the button, enter text in the various fields, etc. Since there's no side effect of consequence until you hit send, you could just make sure your failures clean up drafts, and replaying the whole thing is safe.
I've admittedly done very little browser automation like this though, mainly I've just called APIs, created and uploaded files, done db operations, normal dev stuff.
I'd expect RPA platforms to be way ahead on agent automation like this, I haven't kept with any of them though. If they aren't, real missed opportunity for them.