Raspberry Pi Zero HDMI socket - available current?
If the current limit is not documented, then the only way to determine it is empirically. Get yourself a variable load and plot the voltage-vs-current curve for the HDMI power terminal.

Assuming the circuitry is sophisticated enough to protect itself from overload, you'll find the current limit directly. The shape of the curve will give you some idea of how the current limit is implemented.

Otherwise, you'll reach the dissipation limit of some component on the RPi board, and this will determine the current limit. A thermal imager would be one way to monitor for "hot spots".