Makita Soldering station. I can help you there.
It's 2 3d printed parts, an official Makita spare part (battery connector in the red part), 2 usb-c/usb-a power delivery boards, a pair of switches, and some nuts & bolts.
I did a bodgier version of this some years ago: The cheap Makita widget that gives you a pair of 5V USB-A outputs
[1], modified to present the raw battery output (via a polyfuse) on a 2.1mm DC jack, leaving the USB gubbins intact because it's bound to come in useful. TS-100 soldering iron (I think the first of these style portable irons, from before higher-voltage USB became a common thing, and they assumed people would power them with vehicle batteries and laptop PSUs) plugs into that, and the iron's software handles low-voltage cutoff.
Works well, but then so does a suitable USB battery pack. Which is better probably depends on whether it's primarily about doing a lot of soldering without being tied to a mains socket (eg. when working on vehicle wiring, in a shed, or up a ladder or something) or a neat portable solution you can have with you in case you need to perform a small repair. The killer feature of power tool batteries being that they recharge extremely quickly, and you can have one on charge and one in use.
Have you considered integrating some sort of iron holder? That's the thing that I find most annoying about soldering in odd places - very easy to knock the iron off a little lightweight stand when working at floor level. The battery's enough of a lump that a stand attached to it should mostly stay put.
The other thing that I've failed to research, but is no doubt possible, is some sort of hot air gun that can be powered in the same way. I'm thinking for heatshrink rather than SMD reflow, without going full paint-stripper.
[1] I'm surprised they haven't come out with a newer version that gives you full laptop-spec USB-C PD. That would be awesome.