events won’t have those icons because an event isn’t, by itself, either client or server only. I think icon system is just part of how nodes look, and nodes don’t change based on property changes (like Replication setting) beyond text. I can ask developers to add a more full tooltip for Run on Server option, though, because it could definitely be clearer.
OnClicked event responds to Controller input only, which can only occur on Server or Client that owns it. So while Server instance of Actor could see that it was overlapped by Server instance of character when Client overlaps it (it’s occurring on both Server and Client), when Client controller clicks on it, only Client instance is getting any input, because PlayerControllers only exist on their respective machines. Server instance, which is only instance that could run Run on Server RPC, never saw that Client controller interacted with it (because again, Client controller isn’t replicated and therefore only interacted with Client instance) and thus couldn’t run Server-side event.