Those are outputs, not inputs.
The PocketBeagle 2 uses three ideal diodes (LM73100) in its power path to automatically select one of three available power sources, as shown in the simplified diagram below:

The voltage inputs are:
- USB_5V is available on P1.07 and is also connected to the USB-C port's 5V pin. Valid voltages are between 3.8V and 5.5V.
- VIN_5V is available on P1.01. Valid voltages are between 3.8V and 5.5V.
- VBAT is available on P2.14. Valid voltages are between 3.2V and 4.6V. It is turned off if any of the others are present
VSYS is a voltage output available on all pins labelled 5V on the Gem boards. An external power source should not be connected to it directly. External power sources can be added to the on-board pool of available, mutually exclusively, power sources if connected to VSYS via a diode.
In general, the ideal diode network into VSYS selects the power source with the highest voltage and connects it to VSYS. Each ideal diode has voltage thresholds with hysteresis. A battery charger (BQ21040) is connected to VBAT and can recharge a single-cell Li-Ion or Li-Polymer battery at up to 540mA when USB_5V is available. See https://docs.beagle.cc/boards/pocketbeagle-2/03-design-and-specifications.html and the PocketBeagle 2 schematic for full details. A JST[mention part series]-compatible connector with GND and VBAT is present on the Bela Gem Multi board.
To power the board when a USB-C power source is not available, VBAT should be used for LiPo cells and VIN_5V should be used for any other power source, except as noted below.
REV A4 AND BELOW
On Bela Gem Stereo and Multi boards version A4 and below, the USB-A host port is powered directly from USB_5V. If the USB host port needs to be functional when USB-C power is not available, then an external 5V power source should use USB_5V via a diode. The diode ensures that If USB-C and the external power source are both active at the same time they are not short-circuited. The diode should have a small enough forward voltage to ensure that the voltage at USB_5V remains above 4.45V as per the USB specs. If USB-C power and the external power supply will never be present at the same time, the diode can be bypassed.
REV A5 AND ABOVE
On Bela Gem Stereo and Multi boards version A5 and above, the USB-A host port is powered from VSYS. As such, any voltage in the voltage in the valid range applied via the USB-C cable , USB_5V or VIN_5V will automatically power the USB-A port.