Reason for Phase lead in RC high pass filter
If you want to understand phase relationships of passive filters you have to buy into the right terminology else you will forever be going back to first principles and that first principal is that current flow is determined by capacitance multiplied by the rate of change of applied voltage

If you then apply sinewaves to that first principle you start to see and understand the phase relationships.

So, for ac applications we just remember the simple acronym CIVIL. It stands for Capacitor:I leads V and V leads I in an inductor (L).

We also remember that the impedance of a capacitor reduces as frequency increases and that the impedance of an inductor increase with frequency.

All proven from the basic formulas for capacitors and inductors but conveniently converted to different pictures when thinking about AC analysis and, if you talk about phase shift you are buying into AC analysis.

To talk about charging and discharging in the samesentance as phase shift is missing the point.