Unfortunately, that is how the *arrs are meant to function. Sonarr/Radarr/Lidarr/Readarr are meant to be set & forget. Prowlarr can be used for manual searching, and it is fairly good at it because it is a search aggregator, but if you manually search on Prowlarr, you have bypassed the *arrs and they will not see what you grab, because you necessarily haven't told them that you've grabbed anything. I do not believe Prowlarr is capable of going the other direction, and Prowlarr should be used with the *arr suite because of category searching.
All that to say that, the *arr apps are functioning as intended, it is you that is not conforming to them.
I should also say, that you can search manually in the *arrs, but its fairly tedious.
No shade or anything, just informing.