The Sonos app is currently able to connect to, index, and search a local music library.

Where is your music library stored?

The library is in a free standing WiFi capable hard drive. I have an up-to-date controller, and there is no alpha index along the right hand margin. The old SONOS controller had an alphabetic index. Apple Music does as well. My library is quite large and it takes an unduly long time to scroll through, especially for an individual song.

Sonos has said the alphabetic search for local music libraries will return with a future update.

They said that last May . . .

The Chief Innovation Officer mentioned it in December so at least it’s on their radar:

“Likewise, we know our work is not yet done when it comes to improving usability of Local Music Library, and have heard your feedback around requests such as returning A-Z scrolling and improving queue management. We will provide further updates on this as soon as we are able.”

https://support.sonos.com/en/article/the-new-sonos-app-and-future-feature-updates

Thank you

They have been saying this for a very long time.  I first raised it last summer.  This does not seem very complicated.  For those of us with large local music libraries, it is a totally essential feature.  Without it, my local library is vastly less useful.  Please please get this feature back -- it worked fine in the old app, and it continues to work fine in Sonos S1 (which I still use, fortunately, for the part of my system that can function with S1).