I do not have a ~/Arduino directory so how is this possible?

I do however have a ~/.arduino15 directory and running get.py from within there does correctly install the library into Arduino IDE.

In addition, if I use the IDE to install a new board package, guess where it gets installed? That's right - in ~/.arduino15/packages/esp32/hardware

if you are on a Mac, it's ~/Documents/Arduino/hardware

mkdir -p ~/Documents/Arduino/hardware/espressif
cd ~/Documents/Arduino/hardware/espressif
git clone https://github.com/espressif/arduino-esp32 esp32
cd esp32/tools
python get.py

Restart the IDE and you will see the core when selecting the board as ESP32 Arduino (In Sketchbook)

Yes, but the instructions for Debian also state ~/Arduino.

This is not the case in my experience.

It should be ~/.arduino15. This is confusing for people trying to get things working.

I'm not sure how to explain this better. Custom cores are installed in the sketch folder under subfolder hardware. The same way that libs are installed in subfolder libraries under the same sketch folder (where sketches are being saved by the IDE). Custom cores are not installed under .arduino15, because that folder is managed by the board manager in the IDE. You can believe me or not... maybe go read the official documentation from Arduino

The Mac OS instructions are much more clear as they reference the "Sketch book" and talk about ""Arduino" > "Preferences" > "Sketchbook location"".

None of the Linux instructions mention the sketch book, even though it is critical information in order to make it work.

My work around of running get.py from inside ~/.arduino15/packages/esp32/hardware works well.

If you are told the information about sketch book, I am sure that works well too, but that information is not presented to Linux users.

I suggest you update the webpage to ensure the sketch book information is just as clear for Linux users as for Mac OS.