To partially answer my own question, I have found useful information about the cam webserver API here:
https://github.com/easytarget/esp32-cam-webserver/blob/master/API.md
In short, there are a few other useful endpoints, like /status and /control. In order to change resolution, the uri to access would be http://<IP-ADDRESS>/control?var=framesize&val=8
Not all the commands in the link work, unfortunately (and, quite important, the 'save_prefs' does not) but it can be used to programatically access and save frames at the specific resolution one wants, which is all I need.
It appears that the cam webserver is the standard ESP32 CameraWebServer, but I could not find an official API doc just yet. Some more info here: https://github.com/espressif/arduino-esp32/blob/master/libraries/ESP32/examples/Camera/CameraWebServer/app_httpd.cpp
I find it odd that a simple API documentation of the CameraWebServer is not offered on the product page, it would be most useful.
A