I was able to reduce the code even more:

#!/usr/bin/perl -T
use strict;
use warnings;

use FindBin;

my $whereami = $FindBin::Bin;
open my $fh, '<:encoding(UTF-8)', $whereami or die;
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Note that untainting $whereami before opening the file prevents the error:

$whereami =~ /^(.*)$/ and $whereami = $1;
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Interestingly, removing the :encoding prevents the error, too, without untainting, which seems wrong.