As far as I've checked past threads, I think it's safer to use the NB10000 power bank.
NB10000 has protection circuit and voltage adjustment function.
If you use it as is, the mini PC will not be able to measure the remaining battery power, but it is safe to use it until it is empty.
When using a LiitoKala battery, you can make a more advanced battery status check on your mini PC by creating your own peripheral circuits for protection functions and remaining power measurement.
However, without a protection circuit, there is nothing to measure the voltage or remaining power, so there is a good chance that it could be dangerously discharged and damaged.
It is much easier and safer to use such a cable in combination with the NB10000.
DSD TECH MagicConn SH-CP12B Cavo di Alimentazione USB tipo C da PD a CC-12V
As far as I'm concerned, you need to use a special short connector and flat cable. In that case, Type-C trigger cable is not suitable.
You will need to combine a conversion adapter like the one below with a flat cable.
Adattatore da USB C a DC 12V
I checked the specifications of "LiitoKala" model number "Dii-12V3000" battery from AliExpress.
If what is written is true, I think it is safe for charging and discharging since it has a basic protection circuit.
However, the output voltage remains 12.6V when fully charged and 10.8V when discharge is complete.
If you know the input power specifications of the mini PC, it may be possible to estimate how long it can operate compared to the battery voltage.
If the mini PC can operate in a voltage range wider than battery voltage 10.8-12.6V, you can calculate it just by the mini PC's power consumption and battery capacity "Wh".
If the total power with the LCD monitor is 8W, you can expect a working time of 4.73h.
37.8Wh / 8W ⁼ 4.73h
For example, if the mini PC operates in the voltage range of 11.5 to 13V, the operating time will be shortened to around 3 hours.
You haven't revealed the details of the mini PC so I can't judge.
You can't tell what kind of board it is just by looking at the SoC model number.
What is important is the model number of the board and mini PC product.
Regarding the LCD, as far as I can tell, the power consumption is unknown, so it is impossible to calculate the operating time without experimenting.
Model number "8HP-CAPLCD Monitor"
*Aside from the fact that if you want to calculate it in advance, you should do it before purchasing...
If you already have all the parts, I think it's easiest to actually measure the battery life.
It is possible to measure electricity on a small budget by using a power source such as a Type-C PD compatible charger from a wall outlet.
Type-C power measurement components