Quick Charge requires negotiation over data pins, but the Type H connector has none, so it will only provide up to the USB standard maximum of 500mA until it completes negotiation for more. You can confirm your pinebook is charging at 300-500mA in this state by checking sysfs -- it's only enough to drain the battery more slowly, not charge it.
So to use the USB-to-H wire, you actually need a "dumb" power supply like the provided wall wart that just drives 3A without caring what's on the other end. I know some power supplies meant for SBCs like RPi are like this, but I couldn't tell you how to be sure it's a dumb supply when browsing online, except that Quick Charge or any similar standard is a red flag.
So to use the USB-to-H wire, you actually need a "dumb" power supply like the provided wall wart that just drives 3A without caring what's on the other end. I know some power supplies meant for SBCs like RPi are like this, but I couldn't tell you how to be sure it's a dumb supply when browsing online, except that Quick Charge or any similar standard is a red flag.