The easy approach would be to use Encode::encode to convert your string to octets before writing it to the file:

my $unicode_string = "Smiley Face: \x{263A}\n";
my $bytes = encode('UTF-8', $unicode_string);
binmode $fh, ':raw';
print {$fh} $bytes;
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But I think that the binmode ':utf8' already should do that. Maybe there is a difference between :utf8 and :encoding(UTF-8), so maybe try:

binmode $fh, ':encoding(UTF-8)';
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in your code instead.

But as you already looked at the documentation of IO::Compress::Gzip and it doesn't have a proper binmode implementation, you will need to do that yourself I fear.