Hi saguaros
So I was able to fix it myself after searching... it was a small setting in the modules, on the Advanced tab, the last option at the bottom, the module style. In Joomla 3.10 it was "xhtml", but this does not exist in Joomla 4, so I used "html5" and it worked.
That's something that is not explained in the documentation of JA Alumni. By the way all of the screenshots need updating, as this option (maybe others too) is different from what we find in Joomla 4 version.
▶ I would love to know how to fix the block swapping myself please, as already asked in my previous answer. Thanks a lot.
▶ There is one thing still weird in the frontend, the bottom right button to come back to the top has lost its image.
The website is now live, you can access it with the same login and password as before, just use the root instead of the folder new if you want to access it.
Thank you inadvance for your support, sincerely, Joanie