__________________ | | | | | | | | USB ___________ | computer display |____________________| | | | | powerbank | | |_________ _______| (battery) | |__________________| HDMI | | USB |___________| | | | | .--------^--^. | RPi module | '------------'
A powerbank (f.e. a rechargable battery) commonly has USB ports for powering devices that also have USB ports for being recharged or powered. Raspberry Pi modules [raspberrypi.com] have USB ports for being powered. Less commonly (as of the year 2022), computer displays might have a USB port for being powered by a USB charger, therefore can be powered from a USB port of a powerbank.
Therefore, it can be as simple as "square peg into square hole, round peg into round hole" for suddenly having a portable Raspberry Pi device. Swap out the Raspberry Pi module with a different model, perhaps the Raspberry Pi 400 (built into its own buttonboard) or a Raspberry Pi Zero. Choose a different sized computer display at any time, or maybe have a separate powerbank for the display. Whatever fits for the moment, or for later.
For example:
Fails to power the Sunfounder 13.3 inch display with USB-C to USB-C.
That display needs only 10W, so USB-A (from battery) to USB-C (to display) has worked. (Perhaps a USB-C specification issue?)
Fails to power RPi with certain USB-C cables. Perhaps cables are too long, or maybe need to be of a certain power specification? The short USB-C cable that came with a SanDisk Extreme Portable SSD (250GB, 500GB, or 1TB) has worked for powering the RPi with the Anker 87W battery using USB-C to USB-C.
Possible to power two RPi modules with the USB-C ports, and two monitors with the USB-A ports. However, consider a discrete power source (battery) for a device that needs an exceptional amount of power.
The key is to make sure the powerbank outputs the voltage (V) and amperage (A) expected by the devices, and enough overall wattage (W). The manual for the powerbank, or its manufacturer, should state the output voltage and amperage for each of its ports, and the max total wattage from the powerbank. That info might also be written on the powerbank itself.
Each USB-A port might be 5V and 2A, or it might be 5V and 3A. The USB-C port on a powerbank might have multiple possible voltage/amperage combinations. The manual for the powerbank should state which port is for recharging the powerbank, and how much voltage/amperage it can receive as "input".
As an example, the Anker 87W powerbank has two USB-C ports, and each can deliver power or be used to recharge the powerbank itself. The specifications for each port are conveniently printed (inconveniently very small) on itself, as well as listed in its manual. Unfortunately, the Anker 87W powerbank is unable to power other devices while itself is being recharged.
The maximum power (wattage) needed by a device (f.e. RPi or computer display) is what is usually specified in the manual for the device, perhaps as "Consumption" or "Rated power". A device might actually use much less wattage, perhaps rarely needing the maximum specified, f.e. Raspberry Pi modules tend to be power efficient in that way.
For example, the specifications for the Raspberry Pi modules are provided by the Raspberry Pi manufacturer. Some Raspberry Pi modules want 5V and 2.5A, which means 12.5W output from the powerbank. Though the Rasberry Pi 4 Model B does work with those amounts, they recommend 5V and 3A for it (15W output from the powerbank).