with clipboard output, the äöü, etc are NOT preservec, and I get weird ASCII signs instead of them

Sounds like an encoding mix-up. (The term is "mojibake".) SQLite is internally UTF-8 (unless you take special steps otherwise, which you probably haven't done) so the problem exists downstream of the database itself. I don't know the clip command you're using well, but it apparently expects its input to be encoded in the system codepage, which is almost certainly not UTF-8.

From reading around a bit, I think the easiest fix for you is to stop using clip and instead use a small Powershell script which sets up the relevant encoding(s) and uses Set-Clipboard. Or your batch script can do chcp 65001 (before calling clip) which might help, but be careful with that as I don't know if that's a local-inheritable or global setting; in the latter case, you can get into horrible trouble. (What's actually missing is a command line option to clip to tell it what the encoding of its input really is, but we don't live in that universe.)

Changing the output encoding of the sqlite3.exe program is much harder.

tl;dr: Find a different way to reach your eventual goal. Moving your data via files is far more likely to work, especially if you have a lot of output.

Yori is a (free and open-source) Windows command-line shell and collection of (almost 100) standalone utilities to fully operate with UTF-8.

Example shell session (CMD.EXE) with the default Windows clip.exe program vs. the Yori yclip.exe program to get UTF-8 text to/from the clipboard:

C:\...> echo .q | sqlite3.exe -cmd "SELECT 'äöüÄÖÜ';"
äöüÄÖÜ

C:\...> echo .q | sqlite3.exe -cmd "SELECT 'äöüÄÖÜ';" | clip

C:\...> yclip.exe -p
äöüÄÖÜ

C:\...> echo .q | sqlite3.exe -cmd "SELECT 'äöüÄÖÜ';" | yclip.exe

C:\...> yclip.exe -p
äöüÄÖÜ

Example shell session (CMD.EXE) with the Windows default CMD.EXE type command vs. the Yori ytype.exe program get UTF-8 text to/from a temporary file:

C:\...> echo .q | sqlite3.exe -cmd "SELECT 'äöüÄÖÜ';"
äöüÄÖÜ

C:\...> echo .q | sqlite3.exe -cmd "SELECT 'äöüÄÖÜ';" > temp.txt

C:\...> type temp.txt
äöüÄÖÜ

C:\...> ytype.exe temp.txt
äöüÄÖÜ

(Or just open temp.txt with a text editor.)

Note there's also a patch to enable Unicode input and output for the console on Windows.

How would I

What is the goal? To export certain database rows to files?
Using the clipboard is a bit of a fudge ...

I struggled to follow the steps you've tried - 'file output is very erratic' - it usually works or it doesn't. Do you mean output is as expected but doesn't occur, or it does occur but output isn't as expected. If the output isn't as expected, is that throughout the whole file or just certain records?
It seems you're looking for a solution to problem B when there might be a better solution to problem A.

BTW, Yori's yclip.exe also works from within the SQLite shell:

C:\...> sqlite3.exe
SQLite version 3.38.5 2022-05-06 15:25:27
Enter ".help" for usage hints.
Connected to a transient in-memory database.
Use ".open FILENAME" to reopen on a persistent database.
sqlite> .once | yclip.exe
sqlite> SELECT 'äöüÄÖÜ';
sqlite> .q

C:\...> yclip.exe -p
äöüÄÖÜ

Do people in english speaking countries really say mojibake??

Say it? No. Write it? Yes. Refer to Wikipedia for it? Definitely!

I'm not sure where the issue lies, but the SQLite REPL does seem to not properly handle UTF-8 on Windows.

## Linux
$ sqlite3
SQLite version 3.37.2 2022-01-06 13:25:41
Enter ".help" for usage hints.
Connected to a transient in-memory database.
Use ".open FILENAME" to reopen on a persistent database.
sqlite> select 'Une chaîne aléatoire de choses aléatoires.';
Une chaîne aléatoire de choses aléatoires.

## Windows 11
C:\> chcp
Active code page: 65001

C:\> python3
Python 3.10.5 (tags/v3.10.5:f377153, Jun  6 2022, 16:14:13) [MSC v.1929 64 bit (AMD64)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> print('Une chaîne aléatoire de choses aléatoires.')
Une chaîne aléatoire de choses aléatoires.
>>> exit()

C:\> sqlite3.exe
sqlite-tools-win32-x86-3380500\sqlite3.exe
SQLite version 3.38.5 2022-05-06 15:25:27
Enter ".help" for usage hints.
Connected to a transient in-memory database.
Use ".open FILENAME" to reopen on a persistent database.
sqlite> select 'Une chaîne aléatoire de choses aléatoires.';
';
Une cha
sqlite>

Note that I had to close a mysterious quote on a second line to even get some of the output, it appears the î in chaîne is somehow being decomposed to something that SQLite thinks is a quote. No idea what layer is failing, but Python is doing the right thing in the same environment.

You can use the patch linked in post 5 to fix this.