TLDR: It’s compatible with other copy-left licenses like GPLv3. However, it’s available in multiple languages, which technically makes it more applicable.
I started using it for my own project. If you want a practical example: https://github.com/TimoKats/emmer


I am not an expert in copyright law, which is what these licenses are based upon and cannot analyze the text.
Still, couldn’t you make it even more straightforward by forking twice yourself?
I’d by surprised if the license authors did not consider this. Lawyers wrote this with consideration of EU law after all, not some laypeople.
If I had to guess: Any inclusion of EUPL code in another project would have to be marked as being under the EUPL. This is solely to inform anyone who wants to fork this section and distribute the code in form of SaaS to abide by source code requests.
It’s like an EU variant of the AGPL whose many conditions about linking apparently don’t hold up in EU court. The GPL’s are all primarily considering US copyright law after all.
I think the EUPL has indeed outruled such redistributing-to-oneself by defining
(Besides, I could imagine that even without this definition, such redistributing-to-oneself would already constitute a violation because it would count as an act in bad faith.)
Keeping up copyleft is a neverending struggle against influence campaigns and lobbying operations telling us and telling public officials, “Don’t be so obsessed with copyleft like the ideologues at the FSF are; all those scenarios you’re hearing about up won’t occur anyway.” And then they try to privatize the X Window System. The second document that you linked to (this one) actually has this interesting sentence in the Disclaimer at its top: “The Matrix is not influenced by ideology (telling the good and the ugly, urging people to use or to avoid specific licenses).” It does sound like the authors have been under such an influence.
My theory would be that these lawyers, top professionals doubtless, were being tasked something like “By golly, we have 27 languages, 27 legal systems, and the French are already using their own favorite licence—you have to give us something we can work with”. And so interoperability, convertibility, became their top priority, to which they would indeed consciously or unconsciously sacrifice watertight copyleft.
That being said, the issue with how well the GPL and AGPL fit European jurisdictions must of course be resolved somehow.
Oh, I didn’t consider the “any other” aspect.
Welp, I can still register several distinct legal entities in different EU countries, can’t I? Maybe one could be a “Taking every EUPL work on the internet and relicensing it under LGPL as a service” company. That’s bound to make some money from SaaS companies if it would be this easy to purge the EUPL terms.
Though the “ideology” quote is a bit awful, I’ll give you that. The matrix itself does look fairly neutral though, especially with this part under “Discussion of Linking”:
I’d also argue the 27 legal systems might not be too relevant since copyright law is generally equal in the different member states. The remaining legal issues (e.g. warranty) are irrelevant for interoperabilith between licenses. Also, most importantly, there are only 24 languages in the EU.
If the official guidelines are recognized by courts as legally binding then I think the EUPL is superior to even the AGPL. Sadly that remains to be seen due to the lack of EUPL projects out there (and the lack of corresponding lawsuits).