The USB power pack already contains a boost converter to give 5 V from the 3.5 - 4.2 V that the Li-Ion cells inside it put out, so adding a 5 V to 12 V converter isn't a problem.
Something like
https://www.ebay.co.uk/itm/Mini-Voltage-Converter-Step-Up-Module-5V-8V-9V-12V-Power-Boost-Convert-Module-UK/193540864083 would do.
You need about 300 mA at 12 V for two digits of the LEDs. That will mean about 1 A at the battery, but that seems fine as 10,000 mAh power banks aren't expensive.
You need to control the LED current for each segment. The simplest way is to have a reasonably generous supply voltage, such as 12 V, and put a resistor in series with each segment. The specification says that the LED voltage will be typically 7.8 V, so that leaves 4.2 V across the resistor, so 210 Ohms is needed. That takes no account of tolerances, but would probably be fine. 65% of the power would go to the LED and 35% to the resistor. Brightness will vary if the 12 V supply varies, or the there is voltage drop in any cables, but there is a regulator in every step-up converter, and I don't think you are using long cables to take the LED current.
Another way to control the LED current is with a constant current driver for each segment. There are some ICs that do that for you, such as the AL1794AFE-13 which would interface logic or a microcontroller directly to 4 LED segments, but it is in a package with a pin spacing of 0.5 mm. LED drivers like that will give constant current to the segments, and need less voltage to work. That one only needs 0.5 V, so the supply voltage could be 9 V or so and it would work fine. That would reduce the current taken from the power bank as there is less voltage.
You could have a current-controlled boost circuit for each segment. That is the most efficient, but also the most complicated as it would need an inductor for each segment, and a driver IC, and all the ones that I have seen wouldn't work with a common anode LED display. However, that arrangement would mean that the boost regulator for 12 V wouldn't be needed.