if ($i =~ m/@array2/) {

     print "$i is in array2 - skipping\n";
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That regular expression is m/foo bar quux/ and english for that is "array2 is in $i - skipping\n".    It won't work because you are looking for the string "foo bar quux".

my $regex = "(";
foreach (@array2) {
  $regex .= $_ . "|";
}
$regex .= ")";
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$regex now contains the string "(foo|bar|quux|)" which says to match EITHER "foo" OR "bar" OR "quux" OR "", and EVERY string will match "".

You need something like:

my $regex = "(";
$regex .= join "|", @array2;
$regex .= ")";
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