wrote:
Does the team think this could be recharged by connecting a regulated PSU
to it? And if so, what voltage It might require?

If you can get at the USB 5v input rails and give it 5V, the board should
still charge it. I wouldn't charge the lithium cells directly without
protection, since they could catch fire.

If the power bank is sufficiently generic you might be able to find a
replacement PCB:
https://www.aliexpress.com/wholesale...power+bank+pcb

or more likely transplant the cells into a new case:
https://www.aliexpress.com/wholesale...power+bank+diy
(harder if they're pouch cells than 18650s)

Theo