Both of my USBc power banks have passthrough charging and would work for this. That's the feature you need to look for.
However, keeping a battery bank charged to 100% isn't good for longevity, make sure you get a good name brand one so it doesn't catch fire.
Edit to add: the ecoflow & jackery power banks can also charge their batteries while running something. They can do 120v/240v and run the current nose machine, but they're more expensive