The name says it all. Why are these badges (precognitive and beta) unretired when you can't get them anymore?
2\$\begingroup\$ Just a wild guess: I will assume/believe those badges are not retired badges, because you can still earn them. Just not on this Stack Exchange community. \$\endgroup\$– Henry WH Hack v3.0Jun 21, 2022 at 9:40
1\$\begingroup\$ It turns out my wild guess may have something to it. See this related post on meta.SE meta.stackexchange.com/a/197175 \$\endgroup\$– Henry WH Hack v3.0Jun 21, 2022 at 10:03
This is a side effect of badges being a network-wide system. Badges don't get retired from just one site; they get retired from the network wide badge system as a whole.
The beta badge being retired would imply Stack Exchange has decided it won't give it out anywhere ever again, even on future beta sites. It goes without saying that's not the case.
Although we can no longer earn beta badges here, they're still a part of the network badge system and people can still earn them within the stack exchange system elsewhere in the future, so it's not retired.