SteamOS and Bazzite are "Functionally the same thing".
They are not exactly the same thing, but close enough that Steam itself does not give 2 shits about the difference.
(SteamOS is a customized Arch distro, and Bazzite is a customized Fedora distro. Both are set up with a read only binary filesystem, both use btrfs by default, and both use KDE for the desktop mode.)
I run Bazzite on my GPDWin 4 (2024 version), and it works just fine.
Valve does not officially support GPD handhelds with SteamOS at this time, and is focusing on the ROG Ally instead.
Other than a somewhat screwy accelerometer, the Win4 is actually a better offering than the official steamdeck. (More RAM, better processor, hardware keyboard, etc.)
I am able to run modern and retro titles on it just fine.
The *ISSUE* is going to be the tinkering steps needed for some very retro titles, which may need things like DGVoodoo2 (Old DirectDraw based games that dont play well without extra love and care, or that need Glide emulation), or Joy2Key (Keyboard+Mouse only titles being hamfisted to work on a gamepad, like STALKER), or need a DINPUT filter in the pipeline to work right (Heretic II / Quake for windows, Need4Speed titles, etc, but also modern things that are officially "broken" on steamdeck, like Dragon Age: Inquisition, which work absolutely fine with the filter DLL present.)
This is in addition to the dreaded "But OUR WONDERFUL ANTICHEAT software wants to make indecent liberties that only windows lets us doooooooooo!" many modern game developers are so high on. (Which SteamOS/Proton has problems with. SteamOS has a native version of EasyAntiCheat, but a lot of publishers want to do bespoke dumbassery instead, and brick/ban people that do the "Unforgivable Sin!" of playing on *DREADED LINUX*.)
This is because SteamOS, in its attempt to be Safe_For_Idiots (and please, I am not trying to be elitist or rude, just pointing out that "Highly curated, to the point where all control is removed, because it's scary for users, and they 'get easily confused' and 'set the wrong things'" results in a systemic lack of understanding, coupled with a platform that does everything possible to slap your hands even when you DO understand, and NEED to do something) makes it much more difficult to set up such things to make them work. Bazzite tries to cut both ways, in that it too wants the root filesystem to be a curated read-only thing, with any and all linux userspace things being handled by flatpak, but it *DOES* let you override that and make local patches to it as well (So that you can create a symlink for /snap for instance, for those things that only ever get released in that cursed, unholy manner.)
In both cases, this kind of lockdown stops you from installing useful system functionality, like NFS, or from changing the default compression level options (Both use BTRFS with zst compression, at level 2. Changing this to something tighter, requires editing /etc/fstab which is on the root filesystem, and--- IS READ ONLY.) Naturally, by design, it prevents you from using native distro-curated binaries from the package manager as well.
Again, Bazzite lets you local-patch this, if you jump through all the right byzantine hoops. Actual SteamOS is less forgiving, and just says no.
If Valve goes ahead with this, I hope they offer 2 channels. The first one for the fully curated experience, and the other for "Tinkerer" mode.
Sadly, I feel that the "But our sacred and special anticheat!!!!!" hysterionics will result in any such split channel distro having the latter completely blacklisted by everything, even though the people using it just want to set some quality of life settings. (like the compression level)
The "Users are easily confused and dont understand!" philosophy precludes making these things into easily set GUI options.
To get around this "We applied mittens with duct tape!" curation, and actually manage the system library registrations, and individually tailor proton container instances so that such things as DGVoodoo2 and pals can work, you need to use things like ProtonTricks. This *IS* available as a Flatpak, but it will go against the "Users are easily confused!" mantra.