You don’t need steam os
You can install bazzite and run basically any steam game plus a ton of non steam games. It has much broader hardware support too (which makes sense since valve is building steamos primarily for their hardware)
If you want a small but capable machine pick up an asrock bc250. It’s a blade for mining crypto based on a gpu that’s very similar to a ps5. They’re like $150 or so used. You’ll then need an nvme, a case, a power supply, and something to handle cooling (they’re typically in servers with serious cooling so you have to actively cool the card). Replacing the thermal putty and paste and adding 2 120mm fans is usually good. There are plenty of 3d printed cases you can print/buy that have direct instructions for cooling.
You end up spending about $150 for the card, $125 for accessories like fans/thermals, fan adapter, power supply, DisplayPort to hdmi cable/adapter, usb hub, wifi/bt card, filament for case (a bit more if you have to buy the case and can’t print it), and then whatever an nvme costs (which is tbf skyrocketing, but it uses gen3 nvme which does save a bit). So like $3-400 depending on how big of an nvme, which is less than half of the bottom config steam box with (likely) notably better performance
Stock config can get 60-100fps on most AAA titles at 1080p with high or medium high settings, and is comparable to a 3060 rig. However, the apu on has 24 of 40 compute units open and recently someone figured out that you can sometimes unlock all 40 (though not on all cards, sometimes the extra cus are bad). If you can this boosts performance by sometimes quite a bit depending on what your use case is; for gaming it can be less substantial (~20% increase) but for local llm inference it can be very substantial (~60% increase). This also noticeably increases power draw though and requires more substantial cooling.