What is an "anonymous union variable"? Why would it be captured when attempting to capture a member of an anonymous union?

'Anonymous union variable' is defined in [class.union.anon].

My reasoning here is that non-static data members aren't variables, meaning they can't be (individually) captured. But now that I look at it again, I realize [expr.prim.id.general]/2.2 does not explicitly say that the anonymous union variable in the implied class member access is named with an (invented) id-expression, which is needed for things like [basic.def.odr]/5 and [expr.prim.lambda.capture]/7 to work under this intepretation. So it looks like more changes are needed here, and I'm not entirely sure in which direction (either make the change to [expr.prim.id.general]/2.2, or specify that members of anonymous union variables are themselves local entities); either way, this is probably not editorial.

Since members of anonymous union variables are not local entities (as you correctly observe), they can't be captured to start with.

I think the correct fix is to remove both mentions of anonymous union members (normative duplication) and add a note after [expr.prim.lambda.capture] p1, saying that members of anonymous unions cannot be captured because they are not local entities (xref).

Yes, but the union also needs to be odr-used by an expression naming its member.

Relatedly, members of anonymous unions don't belong to a namespace scope, but [basic.link]/3.3 claims otherwise. And [basic.link]/13 through /15 do not account for anonymous unions either.