Isn't both exactly the other way round?
The license (EUPL-1.2) specifically talks about redistributing either the source, or executable files. (see definition of original work, also distribution.) Nowhere do they mention a service running the work comes with any kinds of obligations? I just can't find any single sentence in the license text covering SaaS...
Both "Copyleft clause" and "Provision of source code" are pretty clear as well. It's only about distributing copies of the work. Not running it and providing it as a service.
And regarding the compatible licenses, they say the other one wins. At least regarding the "obligations". However that's defined and whether it's the licensor's or licensee's obligations:
Should the Licensee's obligations under the Compatible Licence conflict with
his/her obligations under this Licence, the obligations of the Compatible
Licence shall prevail.