Why does my phone pull less current from power bank when the screen is on?
Maybe your power bank or the power management system of the phone itself is not able to supply enough power for charging and power for normal phone operation.

I.e. you may only charge while the phone is in stand-by or operate the phone normally but without charging.
If e.g. charging (+ stand-by) consumes 7W and nomal operation consumes 5W , the power system is, however, only able to provide 10W (but not 12W) you get the behaviour you have described.