In my opinion the schematic is definitely wrong since it shows a net as both 2V5 (on the net) and 3V3 (P1) at the same time plus the part number is for a 3V3 regulator. Sure you can select the voltage what you want but that's not noted anywhere. Asking for trouble in any kind of significant production.

Generally you shouldn't apply a voltage to a regulator's output.

If you are applying 3.3V to BATT and to the "3V3" net on P1 then that is both sides of the regulator if U5 1-2 is connected. Actually ON and ENA are connnected via the jumper U5 so if you have both on 3V3 then that explains completely what you're seeing.

So basically you're applying 3.3V on both in and out of the regulator. Results are "undefined" but unlikely to be anything you can see. That's really the result of your final question. Absolute worst case the regulator might eventually fail and short the OUT line to IN (not issue for you) or ground which will short out your supply. Unlikely though.

This regulator is an inline FET and current sense resistor. So shorting it out won't really do anything to it.