Thanks for the feedback. I don't have a Debian available; I'm running Cygwin with Perlbrew and was able to wind back to v5.32.0 (the closest I have to your v5.32.1). Under that version I have Unicode::UCD 0.75 and Encode 3.06 — what do you have? Here's a few tests.

$ perl -v | head -2 | tail -1
This is perl 5, version 32, subversion 0 (v5.32.0) built for cygwin-th
+read-multi
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I saw the three vowels (WITH DIAERESIS) on the web page. They didn't change when I pasted them onto my command line; nor in the uparse output. However, when I pasted the results back here:

$ uparse äöü

============================================================
String: 'äöü'
============================================================
ä       U+E4     LATIN SMALL LETTER A WITH DIAERESIS
ö       U+F6     LATIN SMALL LETTER O WITH DIAERESIS
ü       U+FC     LATIN SMALL LETTER U WITH DIAERESIS
------------------------------------------------------------

And just so that you know what I'm seeing:

$ uparse äöü

============================================================
String: 'äöü'
============================================================
à      U+C3     LATIN CAPITAL LETTER A WITH TILDE
¤       U+A4     CURRENCY SIGN
à      U+C3     LATIN CAPITAL LETTER A WITH TILDE
¶       U+B6     PILCROW SIGN
à      U+C3     LATIN CAPITAL LETTER A WITH TILDE
¼       U+BC     VULGAR FRACTION ONE QUARTER
------------------------------------------------------------

There were no surprises with my other tests.

$ uparse ���

============================================================
String: '���'
============================================================
�       U+FFFD   REPLACEMENT CHARACTER
�       U+FFFD   REPLACEMENT CHARACTER
�       U+FFFD   REPLACEMENT CHARACTER
------------------------------------------------------------

$ uparse 👨‍🦳‍👧‍👦

============================================================
String: '👨‍🦳‍👧‍👦'
============================================================
👨      U+1F468  MAN
        U+200D   ZERO WIDTH JOINER
🦳      U+1F9B3  EMOJI COMPONENT WHITE HAIR
        U+200D   ZERO WIDTH JOINER
👧      U+1F467  GIRL
        U+200D   ZERO WIDTH JOINER
👦      U+1F466  BOY
------------------------------------------------------------

$ uparse 👨🏽‍✈️

============================================================
String: '👨🏽‍✈️'
============================================================
👨      U+1F468  MAN
🏽      U+1F3FD  EMOJI MODIFIER FITZPATRICK TYPE-4
        U+200D   ZERO WIDTH JOINER
✈       U+2708   AIRPLANE
        U+FE0F   VARIATION SELECTOR-16
------------------------------------------------------------

$ uparse X🩼X

============================================================
String: 'X🩼X'
============================================================
X       U+58     LATIN CAPITAL LETTER X
�       U+1FA7C  <unknown> Perl v5.32.0 supports Unicode 13.0.0
X       U+58     LATIN CAPITAL LETTER X
------------------------------------------------------------

$ uparse `perl -C -e 'print "X\x{1fa7d}X"'`

============================================================
String: 'X🩽X'
============================================================
X       U+58     LATIN CAPITAL LETTER X
�       U+1FA7D  <unknown> Perl v5.32.0 supports Unicode 13.0.0
X       U+58     LATIN CAPITAL LETTER X
------------------------------------------------------------

You mentioned "locale setup" but didn't say what you have. I have:

LANG=en_AU.UTF-8
LC_ALL=en_AU.UTF-8
LC_COLLATE=en_AU.UTF-8
LC_CTYPE=en_AU.UTF-8
LC_MESSAGES=en_AU.UTF-8
LC_MONETARY=en_AU.UTF-8
LC_NUMERIC=en_AU.UTF-8
LC_TIME=en_AU.UTF-8
[download]

That's the best I can do. Perhaps someone with the same O/S and Perl version as you can shed more light on your problem.