if you have a Danish plumber talking to a French electrician on an Italian building site it’s going to be in English
As you can notice, this is not in line with the definition found on Wikipedia. Also, an Italian building site is linguistically clearly not relevant.
Would the community and the variety of English it uses would be any different if instead of a French electrician you had a Turkish or Nepalese one? Because that's a way more likely situation.
Have you tried to address that doubt by doing a literature review, there’s studies going back to at least 2000
Well, I've just read one of the articles used as a reference on WP. It's based on a survey among 65 Erasmus students (not a very wide sample, as the study itself admits), and doesn't sound terribly convinced: https://hrcak.srce.hr/en/clanak/135148 - finding only a few characteristics to be markers of potential "Euro-English" (and, interestingly enough, noting that some of them appear to be arising or at least acceptable in native English too). If you have read something more convincing and systematic than the WP article, feel free to forward it to me.
Also that’s not how you use the plural of English, or do you mean that each of them speak multiple varieties?
Um, have you done a literature review? Yes, that's what "Englishes" is supposed to mean, roughly speaking, it's a commonplace term at this point and it's odd you haven't heard of it: https://en.wikipedia.org/wiki/World_Englishes
Going out on a limb, the Slavic languages are quite steadfast indeed when it comes to number agreement across cases.
I'm not sure what that has to do with the topic at hand. There are next to no cases here, we're talking in English.
Are you speaking Slavo-English?
Do I sound like I speak it? Are there any "Slavo-English" characteristics to my writing that you notice? Pluralising a language name is an odd thing in Slavic languages too (and especially difficult in my native language, due to the same case-number suffix in Nom.sg and Nom.pl), if that's what you're aiming for. I used it because it's already used in English by native speakers.
You do know you're not supposed to just slap an [area/language family] prefixoid onto "English" and call it a day? There is no Slavo-English just because you call it that way, Slavic languages do have similarities that result in similarly mis-learned English, but that doesn't make them all a distinct variety of English, and there remains a number of curious dissimilarities among them (as I've noticed while talking with other native Slavic speakers in English).
If another linguistic group doesn’t mind that kind of construction and adopts it, might that constitute Euro-English?
(Assuming we're talking about the dubiously grammatical "Englishes" here, which you ascribe to Slavic influence - which is incorrect but I'll ignore that for the sake of the argument.) Probably, though there would probably have to be more than one single grammatical phenomenon that gets widely adopted if you want to speak of a full-blown linguistic variety. But it's all pointless to discuss. In practice, it definitely wouldn't go down as you describe. The linguistic group that adopts the construction should be all or most of Europe, going by the name. And that's not very likely to happen, because many speakers would barely be exposed to it at all (do you really think many Frenchmen and Germans hear Slavs speaking English?), and if they heard it they'd immediately notice the form is odd, not in line either with English as they were taught, as they might be inclined to speak due to their native language, or in line with what they hear of English in general, and thus they would reject it. It's a bit like the "would you still love me if I were a worm" sort of question.