I've got no problems with my libraries (I use STM32 and ESP32). Probably, or rather certainly, I've got two core libraries, STM32 and ESP32. Or is it core releases? I think they are defined by Preferences > Settings > Additional boards manager URLs
Is there a simple way just to look up what I've got in my core toolbox without wandering through URLs?
If you compile with verbose output during compilation enabled (in file/preferences), you will see the information (first few lines).
FQBN: arduino:avr:mega
Using board 'mega' from platform in folder: C:\Users\bugge\AppData\Local\Arduino15\packages\arduino\hardware\avr\1.8.6
Using core 'arduino' from platform in folder: C:\Users\bugge\AppData\Local\Arduino15\packages\arduino\hardware\avr\1.8.6
The end of the lines tell you which core (aavr) and core version (1.8.6) is used; yours will obviously be different as the above is for a Mega.
Each board manager URL returns a list of all available versions for a set of boards.
For whatever reason, the IDE Board Manager does not have an option to just show the Installed ones, like the Library Manager does. But with the standard find utility (even through WSL on Windows) you can list them, starting at the OS-specific location of your .arduino15 directory
The additional board URL will only tell the IDE where to find the board package on the web; it does not install it automatically. So the question is if you installed the ESP32 board package after adding the additional board URL (or in short, do you have the option under tools/board to select an ESP32 based board)?