Is there a question?

I for some reason figured I’d be able to charge the battery charger, unplug it after some time, then just use it portably. I was wrong. It needs to be plugged in to use.

You were thinking of a jump pack. Something like this: https://www.amazon.com/AVAPOW-Battery-Portable-23800mAh-Vehicles/dp/B08NPHZV8N/ref=sr_1_6?crid=3S4OQ1RHDHTLI