I wonder how much it last with a power bank.
Some time ago I've got a battery powered soldering iron, the weller BP865CEU.
And I really hate it. The batteries don't last nothing, and they was always discharged when I need it. And I can't use rechargeable batteries, not only because it's not recommended, but because they don't fit inside the battery holder.
This is the main problem with battery powered devices, you have to rely in batteries, which are not so good to store energy for long time.
In my opinion for who need to use a portable soldering iron form time to time, the best option are the butane one.
Butane never discharge, once you have the tank filled, you can keep it on the shelf for months, even years, and it still ready to use.
Even the refill tank don't loose his "charge" over time.
Fuels still the best option for store energy for long time.