It may be a while before an official SteamOS build becomes more widely available for other handhelds. Bazzite is decent, but not nearly as feature-rich as the real deal. However, YouTuber and handheld expert The Phawx has successfully managed to get SteamOS 3.8 working on an Asus ROG Ally.
Most SteamOS functions appear to be working well. It recognizes the ROG Ally's 120 Hz panel and even has a toggle switch for VRR. However, the TDP slider, seems to be stuck at 15 Watts and the controller isn't recognized properly, resulting in the back paddles being dysfunctional. This is a relatively early version of SteamOS, so it will require some work before it lands on other devices.
Performance-wise, the Steam Deck's custom Van Gogh APU outperforms the ROG Ally's Ryzen Z1 Extreme despite being a generation older and packing weaker hardware. One can attribute this to Valve's software optimizations for the Steam Deck.
Of course, this will change with the Ryzen Z2 and Ryzen Z2 Extreme are out and about, but OEM-specific under-the-hood work will determine which one will be the best bang for your buck.
Source(s)
YouTube