As far as I know, there are no groups or organizations that have adopted "Perl6" other than hobbyist clubs.
I guess that's probably correct, although the term "hobbyist clubs" seems a bit deragotary here.
It is not a production-ready language ...
Pure prejudiced opinion, at variance with facts
... still breaks backwards compatibility with new releases,
I do not know such case (except for very minor fixes or adaptation to new Unicode standards), perhaps you can enlighten us.
... has a dearth of library extensions for doing real work
Well I agree that the P6 ecosystem is not as rich and as mature as the P5 CPAN, but there are many hundreds of modules for almost everything useful. See https://modules.perl6.org/
. And you can use most P5 modules in Perl 6, as well as Python, C and Java libraries (much more easily than it would be in P5).
... and is orders of magnitude slower than using Perl for the things it can do...
You should update your information, that may have been true 3 or 4 years ago, but that's no longer true. P6 might still be slightly slower than P5 for quite a few things (and may be faster for others), but it's certainly not "orders of magnitude" behind in terms of speed.
but it really doesn't have much to do with Perl
Not true. These two languages are different programming languages, but they are very close to each other, like brothers and sisters.
On the issue of the similar names, well, yes, perhaps, it may be unfortunate, things evolved in an unpredicted way. I am afraid it will probably be difficult to change it now.
To the OP: for the sake of full disclosure, I am the author of one of the Perl 6 books, so I may have my own prejudices. But 1nickt has been known here as a regular staunch opponent to P6, and may have his own. But I guess you discovered by yourself that we disagree on that.
Update: fixed a couple of minor typos.