Why is the "˙" not printing correctly here in my terminal?

Your terminal expects UTF-8. You printed chr(0xFF), which is not the UTF-8 encoding of "˙".

You can encode it yourself, or you ask Perl to do it using the following:

use open ':std', ':encoding(UTF-8)';
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ord() returns 255 for ˙, a single byte. Encode thinks this is utf-8, but isn't this actually utf-16?

It's not UTF-8 (which would be C3 BF). is_utf8($string) does not indicate whether $string contains UTF-8.

It's not UTF-16 (which would be 00 FF or FF 00 depending on endianness).

Decoding string (as use utf8; does for literals) results in Unicode Code Points ("˙" is U+00FF).

This actually looks like valid UTF-8 to me and Encode agrees. Is that correct?

That is the UTF-8 encoding of "Queensr˙che", though it is incorrect to say that is_utf8 signifies that Encode agrees.

Text::Unaccent::PurePerl does not "unaccent" it properly. Why not?

Tools that work with text (such as regular expressions and Text::Unaccent::PurePerl) usually expect the text to be provided as strings of Unicode Code Points, not encoded using UTF-8.

Is there a way to safely convert them to the same encoding?

Aformentioned

use open ':std', ':encoding(UTF-8)';
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use utf8;
use encoding ':std', ':encoding(UTF-8)';

use JSON::XS qw( decode_json encode_json );

my $s = "Queensr˙che";
printf("U+%v04X %s\n", $s, $s);

{
   # Uses encoding specified by "use open".
   open(my $fh, '>', 'foo.txt') or die $!;
   print($fh "$s\n");
}

{
   # Uses encoding specified by "use open".
   open(my $fh, '<', 'foo.txt') or die $!;
   chomp( my $got = <$fh> );
   printf("U+%v04X %s\n", $got, $got);
}

{
   # :raw overrides default encoding specified above
   # since encode_json already encodes using UTF-8
   open(my $fh, '>:raw', 'foo.json') or die $!;
   print($fh encode_json( { text => $s } ));
}

{
   my $json = do {
      # Similarly, decode_json expects UTF-8.
      open(my $fh, '<:raw', 'foo.json') or die $!;
      local $/;
      <$fh>
   };
   my $got = decode_json($json)->{text};
   printf("U+%v04X %s\n", $got, $got);
}
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