What's between \Q and \E is treated as normal characters, not regexp characters. For example,

'.' =~ /./;      # match
'a' =~ /./;      # match
'.' =~ /\Q.\E/;  # match
'a' =~ /\Q.\E/;  # no match
[download]

It doesn't stop variables from being interpolated.

$search = '.';
'.' =~ /$search/;      # match
'a' =~ /$search/;      # match
'.' =~ /\Q$search\E/;  # match
'a' =~ /\Q$search\E/;  # no match
[download]

By the way, I think you want
"s{\\Q\$in\\E}{\$out}g"
instead of
"s{\\Q$in\\E}{$out}g"
The difference will be seen when $in or $out contains a '$'.