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If it is not in the list of extensions, it is not installed.

Pressing install is supposed to show extension file at

/Users/maxi/Library/Application Support/Blender/3.6/scripts/addons/pribambase/aseprite/pribambase_aseprite.aseprite-extension

Which is installed like any other aseprite extension: by dragging into the window, or double clicking, or from preferences > extensions > install.

I added it manually, and sync popped up. Thanks for the help!