Streaming services such as Spotify and Apple have huge catalogs. I listen to Classical exclusively and generally am able between the 2 to find any recording, provided it is in print.
Several caveats apply. Both services have search engines optimized for non classical. There are many times that the Verdi scenario you described happens, even if you type in the names of the Conductor, performers, etc. with repeated search attempts you will hit paydirt, but it can be frustrating. And don’t even think of having Siri find the correct recording; Apple voice recognition is god awful. Amazon might be better with Alexa, but somehow I doubt that it will be attuned to the subtleties of navigating a Classical catalog, and I have found Amazon Music to have less depth of catalog for Classical compared to Spotify or Apple Music.
The next caveat is sound quality, as all the services mentioned are essentially MP3 quality. They can still sound pretty darn good, but pale in comparison to High Rez Streaming. If you live in the U. s., High Rez Streaming means eithe Primephonic, which has a very limited catalog, or Tidal, which is poorly organized for Classical and doesn’t begin to approach the breadth of catalog of Apple or Spotify