Here is somewhat simplified, but untested code , in an attempt to steer you toward more idiomatic code:

my @officialannotation = (); # An empty list. NOT [] , which is an emp
+ty array-ref
my $offgenes;

open(my $infile , "<", "genbankfile.txt") or die "cannot open file gen
+bankfile.txt $!";
while(<$infile>) {
   $offgenes++ if ($_ =~ /\d+/) ;
   my ($start, $stop)  = split;
   push @officialannotation, {start=> $start, stop => $stop};
}
close $infile;
#.. collect the other one in the same way
# Then compare the 2 arrays of hashrefs :

for my $p (@prodigalannotation){
   next unless my ($candidate) = grep {$p->{start} eq $_->{start}} @of
+ficialannotation;
   $exactmatching++ if $candidate->{stop}  eq $p->{stop};
}
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Note - there are many assumptions of the data, and no error checking, and inefficiencies, so this code is far from ideal, but I offer it as an incremental improvement on the OP.