How to Search my vault for all notes which a) contain a property which includes “string” AND, B) whose property that includes string has a value that includes “OtherString”?

See if this matches your expectations:
[/.*?String/: /OtherString/]

Explanation:
Regular expression mode switched on with pair of / in both key and value places.

.*? in regex layman’s terms means you either have anything before String or not; good for cases where you have word compounds and you want to make a qualifier optional.


Related:

For the value part, /OtherString/, see also this thread with my workaround:

In our current case, though, the closing / had to be applied in both key and value places.