There are many billions of Euro worth of renovation, modernization and simplification in the Mittlestand.

There are, the moment the famous Mittelstand realizes the need for that. Until that happens, it is an uphill struggle.

Are they rummaging through old computer parts to fix their old machines like Japan does?

Well, I mean you are trying to get them from Cobol 1.0 to Cobol 2.0. I'd be hesitant as well.

I understand why everything else is suboptimal but why do you want them to migrate from Cobol to Java? What problem is that going to solve for them?

It's about human capital.

Not that I favor Java, or even that I dislike Cobol.

It is rather their existing human capital that makes anything more fancy than Java even harder to migrate to. At the same time, job postings looking for Cobol-Devs in 2020 are useless and even if they manage to find people capable and willing to work with Cobol per se, their existing code-base is an additional deterrant. This further fossilizes what ever ounce of agility their dev teams might have had.

Isn't it the 'legacy' systems are supposed to be left operating as-is, almost like black boxes with defined properties? Some kind of a known seam in the process. Meanwhile, all extensions to process are to be handled by other means.

Given the current capacities, there could be additional layers added to filter or enhance whatever comes out of the legacy processes.

Sure, there needs to be a "keeper" for those legacy systems, but migrating off them may be asking for too much of a manager's beef to get an approval to accomplish.