There’s quite a few. Steam deck and Asus, as you mentioned, but there’s also AyaNeo, GPD, OneXPlayer, Aokzoe, Lenovo, etc. And many of these brands have several different models, if you’re counting individual products.
Anecdotally, I have an Aya Neo. I know a few people with a few of the others brands. There’s a decently sized Aya Neo Discord that I’m part of, and I would assume the other brands have something similar. There’s definitely use of non-Steam handhelds, or there wouldn’t be a growing market for them.
Why more PC gaming handhelds should ditch Windows for SteamOS (arstechnica.com)