And it is ridiculous and embarrassing - imho - that I should give up on that just because they do not allow me to update - And I am really scared that I shall lose my work from the recent years.
You purchased a professional application and are entitled to the compatibility update Aperture 3.6 for the current system on your new Mac.
And with your new Mac you will have have free Apple Support a a limited time. I#d use that to get all the help you can get.
I just tested and installed Aperture 3.4.5 on my El Capitan system.
if all fails you can get it to run on El Capitan, but it has many issues.
Ctrl-click the Aperture application icon, select Show Package Contents, and then launch the executable inside directly.

It will open and you can edit, but it would be much preferable to get the compatibility update installed.

There is no Apple supplied download for Aperture 3.6 other than the AppStore.