Some more datapoints; got a 16000mAh Deltaco PB (PB-815). Rated 3A total (1x 1A port + 2x 2.1A ports). Using the cable coming with the pro controller, it could not charge while playing Zelda when the Switch was at ~60%.
Later I tested to see if it would at least lower the drainage of the Switch battery. The result was when the Switch was fully charged it drained the PB first. Got something around 3h using about 75-85% of the PB.
This is interesting. So essentially you are saying the Switch will drain a portable charger first (when fully charged/does it have to be fully charged?) and then its own battery?
Going by this, you would have been able to use the Switch for about 6-7 hours total using the PB you have and the Switch's battery before having to recharge anything at all?