I'm admittedly angry with Microsoft Edge at this point. That's the nicest way I can put it. Chromium spoon-feeds AVIF support to Edge automatically. Then, each release, Microsoft goes out of their way to deliberately remove AVIF support. Sometimes they remove it too late, and it slips into the Edge Betas (as documented below in Charles Roper's answer).
AVIF is an open, royalty-free image file format. Open source projects have no apprehension including support for it (ie. Firefox, Chromium). You'll find AVIF supported in all MODERN web browsers. There is no legitimate excuse for its exclusion from Edge. It certainly doesn't serve the user's, or web developer's, best interests. With no official explanation, we can only speculate the real reason for AVIF's exclusion.
There's obviously not enough people complaining about this. The issue is known, ignored, and remains open indefinitely.
If you'd like to express your own frustration, as I've done multiple times, open Microsoft Edge and press shift-alt-I (or go to the "..." menu > Help and Feedback > Send feedback). Admittedly, I've been completely ignored by this method, but maybe I'm not enough demand to even be seen.