If I had to guess, searching by genre isn’t available because your search would result in MILLIONS of songs being listed from every music service you have added to Sonos. Imagine searching for “rock” under “Genre” and the amount of results you would get. Not to mention searching by genre from a library of tens of millions of songs is just inefficient and pointless.

But the Sonos app does allow you to search by genre if you set up your personal music library from your computer or NAS.

Whether a music service supports a given category (eg “genre”) depends on that music service, and Spotify does not support Genre search (nor does iHeartradio). In fact I can’t find one that does from my services. Local Library is the only source I have that can do this.