Are there any you could recommend? Most that I have looked at cost about the same or more as a Pi in the first place and don't even come with batteries.
I did some research into this as well and I'd gladly consider this as an option but most power banks can't do this. And the ones that do don't tend to advertise it. Every time someone says they found one that can do this, in some forum or whatever, they are no longer available to buy.