Non-ASCII output after restarting the Perl debugge

Question

[EDIT: It turns out that the original version of this question contained two different issues masquerading as one. (I realized this only after reading and working through tripleee's comment.) Therefore, I split the original question into two. I edited this post to include the issue I figured out thanks to tripleee's comment, and posted the second one here. BTW, that second post incorporates the fix I came with to the problem described in this post, namely setting STDOUT's encoding explicitly within the script, using binmode.]

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I'll use the short demo script below to illustrate the problem.

# -*- coding: utf-8 -*-
use strict;
use feature 'unicode_strings';
use POSIX 'locale_h';
use locale;
use utf8;

setlocale( LC_CTYPE, 'de_DE.UTF-8' );

my $non_ascii = 'ßäöüÄÖÜ';
print "$non_ascii\n";

my @non_ascii = split //, $non_ascii;
print "$_\n" for @non_ascii;

$DB::single = 1; 1;  # return control to DB

(The last line is effectively a breakpoint.)

OK, now I run this under the Perl debugger:

% perl -C -d dbtest.pl

Loading DB routines from perl5db.pl version 1.37
Editor support available.

Enter h or 'h h' for help, or 'man perldebug' for more help.

main::(dbtest.pl:8):            setlocale( LC_CTYPE, 'de_DE.UTF-8' );
  DB<1> c
ßäöüÄÖÜ
ß
ä
ö
ü
Ä
Ö
Ü
main::(dbtest.pl:17):           $DB::single = 1; 1;  # return control to DB
  DB<1> 

So far so good: the script produced the expected output, and now the debugger has entered into single-step mode, and is waiting for input.

If I now just restart the debugger with R, and run the script again (with c, exactly as before), this is what happens:

  DB<1> R
Warning: some settings and command-line options may be lost!

Loading DB routines from perl5db.pl version 1.37
Editor support available.

Enter h or 'h h' for help, or 'man perldebug' for more help.

main::(dbtest.pl:8):            setlocale( LC_CTYPE, 'de_DE.UTF-8' );
  DB<1> c
\337\344\366\374\304\326\334
\337
\344
\366
\374
\304
\326
\334
main::(dbtest.pl:17):           $DB::single = 1; 1;  # return control to DB
  DB<1>

Furthermore, now print no longer produces human-readable output:

  DB<1> print $non_ascii
\337\344\366\374\304\326\334

How can keep the output looking human-readable after a restart?