my, in this context, is of course an erroneous “bareword.”

Not at all. In Perl, declarations can simply used as expressions, they return the variables they declare.

If my was a bareword here, it would violate the "no two terms in a row" rule:

$ perl -ce '"my" $y'
Scalar found where operator expected at -e line 1, near ""my" $y"
        (Missing operator before  $y?)
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It is perfectly legal to write things like

say my $x = 5;
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Which declares variable $x, returns its value, and then prints it, followed by a newline.

I don't see the reason for using such a declaration in the if-statement without any initialization (it will always be undef), but it is perfectly legal.