This smells a little XY Problem to me since I can't see why you'd want to do that.
That said, what's happening here is that the value of $1 is interpolated into $out at the time that you define $out. If you want, you can use single quotes to define out, and it will have the literal string "$1" in it, but that won't work either.
You may be able to do this:
my $out = '/s/Products/$1';
$ENV{REQUEST_URI} =~ s/$in/eval qq{"$out"}/ie;
I can't say I recommend that, however, especially if you don't trust the source of your real $out.
So what problem are you really trying to solve? What lead you to write code like this in the first place?
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