I wasn't able to get the esp32-c3 working although I could compile just could not upload and get it working from there.
To get the ESP-mini32 working I had to first use the webUI linked in the readme and from there I setup Wifi and had it online and the web page loaded. The ESP-Mini32 does not have exposed pins 12 and 13 so I had to edit file src/ElegooCC.h and change pin 12 to 21 and pin 13 to 22. They are on the same side as VCC/5V and GND and in the same row.
Once compiled I copied firmware.bin to my Dowloads folder and used the Upload option in the web page on the device, selected "Firmware" option(default) and then selected the file and uploaded.

I tested with a piece of filament at my desk and started a print while watching the log output on the web page and it showed filament stopping and starting and the connection to the CC. On filament stop the print pauses and can be restarted in OrcaSlicer device page, on filament run-out it paused after a period, I then ran the load command at the printer and then unpaused the print and ran fine.

`[env:esp32-dev]
board = esp32dev
platform = ${common.platform}
framework = ${common.framework}
lib_compat_mode = strict
board_build.filesystem = littlefs
build_flags =
${common.build_flags}
-D CORE_DEBUG_LEVEL=0
${env.build_flags}
-D BOARD_FLASH_SIZE="4M"
-D LTO
-D Os
lib_deps =
${common.lib_deps}

`Looks like: