The feature you want is called pass-through charging by some. It's not typically incorporated in "power banks" because it's not good for the battery.

You may wish to consider a commercial UPS (examples) for this function. The battery is either charging (normal), or discharging when the AC power is out.

Another commercial product that may accomplish this is a dual redundant power supply ([example])(https://www.jameco.com/Jameco/Products/ProdDS/2304391.pdf).

Still another way is to use a "wired-OR" power arrangement to supply power to your RPi. There were some answers posted recently that described how that works: Answer 1, Answer 2

The feature you want is called pass-through charging by some. It's not typically incorporated in "power banks" because it's not good for the battery.

You may wish to consider a commercial UPS (examples) for this function. The battery is either charging (normal), or discharging if the AC power is disconnected.

Another commercial product that may accomplish this is a dual redundant power supply ([example])(https://www.jameco.com/Jameco/Products/ProdDS/2304391.pdf).

Still another way is to use a "wired-OR" power arrangement to supply power to your RPi. There were some answers posted recently that described how that works: Answer 1, Answer 2