Sadly the issue with this is that you can offset both the cost and the carbon impact in just few years. (I say sadly because of course I'd much rather people would reuse than put working hardware to trash)
My T100TA has the processing power of an Raspberry Pi 4 and only consumes <10W.
It's mobile Hardware in the end and thus already optimized.
If you want to save power get a used Atom (like the one in my T100TA).
The are also very cheap.
A Dell Wyse 3040 (2GB RAM fixed) for example consumes 4W idling and < 10W under max load.
CPU Power is a bit better then the Raspberry Pi 4.
And it's only 40€/$
Buying appropriately sized, used hardware will have a better footprint.
That 'carbon impact' is negligible - if even worth thinking about - compared to the environmental impact (which, remember, is totally unrelated to 'carbon impact') of creating that hardware in the first place. If you have something lying around which can be used and it does not come with an onerous power bill, jet-engine fans, vacuum tubes in a fridge-sized cabinet (although that would certainly have some charm) or unobtainable parts by all means use it instead of a new SBC. I use a number of old mobile devices in this way where I would otherwise have employed SBCs. They come with their own UPS, a complete sensor set, cameras, microphones, several wireless interfacing possibilities and some of them even have a screen. Power consumption is minimal and they tend to work fine on whatever USB charger you connect them to where some SBCs are quite picky when it comes to their power supplies. Mobile devices are lacking when it comes to interfaces, they tend to have a single USB connector which doubles as a power input and as such is already occupied so if you need those GPIO pins or USB3 connectors get yourself an SBC without fretting over any 'carbon impact'.
If you want to save power get a used Atom (like the one in my T100TA). The are also very cheap. A Dell Wyse 3040 (2GB RAM fixed) for example consumes 4W idling and < 10W under max load. CPU Power is a bit better then the Raspberry Pi 4. And it's only 40€/$
Buying appropriately sized, used hardware will have a better footprint.