Yeah, you need more than just a power supply. That being said, even low level armor had a fair bit of protection, so if you aren't trying to run it 24/7, you could easily ration it out for dangerous environments or impending combat, and use public recharge stations when you have a chance. This is assuming you're not out in the unexplored vast, away from all civilization, since you have no ship. If you are, you'll need to ration more carefully.
If you are that remote from civilization, the GM should also encourage you to use relevant technical skills to improvise alternate means of recharging your life support systems.
They need to expand on this in the personal items or even technical items page. A portable environmental recharge would be a wonderful item but i can see why it is that way in the rules. Even the Mobile Hostiller acts as a enviromental system for almost a week and its 50credits.
Yeah, there isn't really a difference between recharging powered items/batteries/etc and an armor's environmental protections, in-game wise.
I wouldn't be surprised if various GMs home brewed up something, there's been a lot of talk about it over the months. But as far as actual rules, nope.
Best to ask your GM if you'd rather not find out the hard way.
I look at it as the difference between a normal wall outlet you find pretty much anywhere with electricity and that of a Tesla charging station.
Right now, as far as I can see the Pact Worlds hasn't invented a portable piece of tech that would allow you to convert the wall outlet to function with the Tesla. That said, I'm not sure it's a huge problem because from what I can tell the idea that you can eventually run out of power on your environmental systems for armor seems intentional and not something that is meant to be easily bypassed without returning to a ship or civilization.
The only real rule I know of has been quoted, which says:
The duration of a suit’s environmental protections does not need to be expended all at once, but it must be expended in 1-hour increments. Recharging this duration requires access to a functioning starship or an environment recharging station (publicly available in most technologically advanced or average settlements) and takes 1 minute per day recharged. Most of the recharging stations that replenish devices, such as batteries and power cells, also recharge suits is typically free of price. All other functions on a suit of armor with no duration remaining still work normally.
Otherwise the rules just don't elaborate too much on the topic. When I read it it sounds like you need a specific "environmental recharging station" which happen to be available at almost any battery recharging station you might find (maybe not on Eox). So the ability to recharge a battery does not seem like it would recharge your environmental protections.