I'm not too sure you're correct regarding the UPS not being ok for the 4w. devices. I assumed it depleted what was drawn. I use an old UPS to power my router and phone and it worked fine for a 2day outage.
That's good to know! Do you recall the model and/or size of your UPS? I may need to look for that one.
I've got an APC SUA1000 for my computer. It's a 670 Watt 1000 VA UPS.
They provide a web page for estimating runtime, at
SUA1000 Features. It says the min-max range is 67-670W. When I put in 4W, it says, "The total load (power draw) entered is less than the minimum value for this product (67 W)." Not sure exactly what that means; will it not work, or is it just that they don't recommend it?
I also looked at the
Jackery Explorer 160 Portable Power Station (which looks pretty nice!), but it automatically powers off after 6 hours if drawing less than 10W.
So it appears the behavior depends a lot on the particular model.