You said:

my $line3 = <$hash{'handle'}>;
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Perl interprets <$hash{handle}> as this: glob(qq<$hash{handle}>), which is not what you want, and it's why you're getting the glob ref itself printing.

As stated, you can use readline(), or extract out the handle before you use it:

my $fh = $hash{handle};
my $text = <$fh>;
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