Global saved searches cannot be edited or deleted on the homepage. Trying to edit a saved search duplicates it and trying to delete it does nothing. This can cause an issue if there is an intensive search that is duplicated and using more cycles.
Workaround: it can still be deleted in the global config file.

This isn't a regression, so it is not release blocking. IIRC @slimsag worked on saved searches, so going to assign to him.
I don't know who added those edit/etc buttons on the homepage. AFAIK, usually you can only edit saved searches through the searches page. I bet if you did it there, it would work fine.
Actually, @vanesa this is likely a frontend bug and probably not too difficult to fix. The payoff is rather good for us as well (i.e. having a bug on our search homepage sucks). Would you maybe be interested in taking a try at fixing this?