Yeah, the SearchBox element has always been a bit different from almost everything else in Bubble…
You can do this using a variable to define a User (i.e. current User) when the Current user Is Partner yes, and leaving it empty otherwise, then use that variable value in your search (with ignore empty constraints).
However, that’s not a secure method. (It’s a great method to eliminate the need for conditional datasources generally - but probably not advisable in this case, at least not on it’s own).
Better to do this directly with privacy rules (which you should be using anyway).