I rather suspect that both have been available since Perl 5.000

You could well be right. The "old" label is more referring to when it was in more common use. Back in the day it was everywhere and if that's what you read then that's what you write. I guess the more that I developed as a Perl programmer the more I dealt with complex data structures and the ever more unwieldy the old syntax became. No idea if that's a general thing or specific to me but it's the most likely reason I can see looking back.

Except in the simplest of cases, I'll always prefer the $hashref->{key} form, as I find it both easier to read and less error-prone. I can't think of any situation where the $$hashref{key} form is "required".

Completely agree on this.