If $pattern_str is plain text and not a regular expression, you'll need to convert/escape it before you can use it as a regular expression.

$str =~ /\Q$text\E/
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or

my $re = quotemeta($text);
$str =~ /$re/
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or

index($str, $text) >= 0
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References:
perlre (for regular expressions in general and \Q..\E specifically)
quotemeta
index