I strongly advise you use strictures (use strict; use warnings;) which would have told you about the syntax error in my $func_ref = %hash{"my_function"};. Using & to call a sub is somewhat out of favor. The following may get you sorted out:

use strict;
use warnings;

my %hash = (hello => "Hello World\n", my_function => \&my_func);
my $funcref = $hash{my_function};

&$funcref (\%hash);
$funcref->(\%hash);

sub my_func {
    my $hashref = shift;
    
    print $hashref->{hello}
}
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Prints:

Hello World
Hello World
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