Storage location of the game saves

Where do games save their scores?

I would like to save this file.
If you are wondering: Why?

Because I want to switch from the Intel version back to the ARM version on my MacBook Pro.

The last time I switched from ARM (didn't work properly) to Intel, all the game saves were gone.
And I want to prevent this before I try the ARM version again.

Many thanks

Translated with DeepL.