K7ITM wrote:

SNIPPED ... Agree a capacitor tunes an 'long' antenna to resonance.

When that physically long but electrically shortened to resonance
antenna is excited and a standing wave pattern develops, what is the
phase shift of the current through the loading capacitor? Is the
standing wave current on the two sides of the capacitor different, in a
manner similar to how it's different in a loading coil?

SNIPPED

What's this current phase shift through a capacitor?

I believe it is a voltage phenomena. The incident and reflected waves
induce voltage at the capacitor terminals. In HF systems the capacitor
is very physically small, and the lumped model should suffice. [There is
no long length of wire to confuse the model].

A vertical antenna has a characteristic impedance, depending on ground
effects, proximity effects, etc. of somewhere between 200 and 500 ohms,
typically 350 +/- ohms.[ It's been a long time since I calculated the
nominal value, but for basic understanding just use antenna Zo]. Apply a
stimulus to the antenna and the signal propagates along the antenna
governed by it's Zo. [Not the Zo of the transmission line at this
point]. So, at the incident input side of the capacitor there is a v
that is the integral of current [incident] times time. This voltage lags
the incident current. At the reflected input side there is a voltage
that is the integral of I [reflected] times time. This current is the
reflected value and spatially delayed by the propagation time from the
capacitor to the end of the antenna. This voltage lags the reflected
current.

The net voltage across the capacitor is the spatial sum, NOTE: Spatial
Sum, of the two voltages. Assuming To at the incident current input to
the capacitor then the problem is simplified to the spatial [propagation
delay to the end of the antenna and return].

So, current phase shift in the capacitor may be asking the wrong question.