I've used a Jackery 500 which both powers and charges the Seestar using a USB port on the unit.
Normally I use a FlashFish E200. The Flashfish does not charge the Seestar if using a direct USB connection. However, if you use a wall USB charger plugged into the AC port it will power and charge the Seestar.
Ify our power supply has an AC outlet, you might try plugging in a wall charger and see if that works.
Don