Edit: just checked - it's indeed possible with Android 14. Connecting a mouse doesn't require any confirmation. As long as the phone is unlocked, you can adjust the USB settings with that mouse.
It's probably safe enough to recharge your battery pack and charge the phone off that, even at the same time if supported.
If you already had it on, you could probably use it own the device pretty quick, but it's not enabled by default.
"""To connect a Bluetooth device:
1. Go to Settings > Accessibility, and select Touch.
2. Select AssistiveTouch > Devices, then select Bluetooth Devices.
3. Select your device from the list."""
Is this requirement a very recent change?
(I don't have my own iPad with me right now, but I don't recall enabling AssistiveTouch to get the Logitech keyboard+trackpad working.)
EDIT: I looked online and apparently prior to 13.4 AssistiveTouch was required to use a mouse. But now you don't need it if you only want basic mouse functionality.