A Library on an external drive is not searchable by Spotlight. Searching a Photos Library is a complex thing. Pictures in Photos are not exactly files-- they are combinations of original files with information in a relational database. The original files don't even keep their imported file names, but rather they use Universally Unique Identifiers, so searching for file names can only be done inside the database. 3rd party file searchers, like Find Any File, can't do it at all. Searching a Photos Library means searching through the Photos database. It's only in very recent OSs that Spotlight has been able to search a Library on the internal drive. An external Library is a bridge too far.
However, the internal Library searches work as normal, so for me, at least, it hasn't been an issue. You might look into the trusted 3rd party app PowerPhotos ($35) which keeps its own database of all the pictures in all your Libraries, and it handles searches over multiple Libraries. I use it every day.
You can let Apple know your suggestions here:
Feedback - Photos - Apple
I think that you're the first person I've seen here to bring this up, so it may not be at the top of Apple's list of things to do.
