Hi Saku,
... thank you for your assistance.
I shy away from just installing the binary, as I have multiple machines running and want a proper setup, that is automatically updateable.

For the time being I startet out with this (https://www.cqrlog.com/node/4644) approach of installing mysql-server and cqrlog first and then reverting to mariadb-server.

However, this is where the shit hits the fan:

• There appears to be some trouble with the mysql-server unit file, that I do not understand
• Hence the installation of mysql-server does not run properly though and
• hence I cannot replace it by mariadb-server

I have now the following:
# apt-get install mariadb-server
Paketlisten werden gelesen… Fertig
Abhängigkeitsbaum wird aufgebaut… Fertig
Statusinformationen werden eingelesen… Fertig
Die folgenden zusätzlichen Pakete werden installiert:
galera-4 libconfig-inifiles-perl libdbd-mysql-perl libdbi-perl
libmysqlclient21 mariadb-client mariadb-client-core
mariadb-plugin-provider-bzip2 mariadb-plugin-provider-lz4
mariadb-plugin-provider-lzma mariadb-plugin-provider-lzo
mariadb-plugin-provider-snappy mariadb-server-core pv socat
Vorgeschlagene Pakete:
libnet-daemon-perl libsql-statement-perl mailx mariadb-test
Die folgenden Pakete werden ENTFERNT:
default-mysql-client-core default-mysql-server default-mysql-server-core
mysql-client-8.0 mysql-client-core-8.0 mysql-server-8.0
mysql-server-core-8.0
Die folgenden NEUEN Pakete werden installiert:
galera-4 libconfig-inifiles-perl libdbd-mysql-perl libdbi-perl
libmysqlclient21 mariadb-client mariadb-client-core
mariadb-plugin-provider-bzip2 mariadb-plugin-provider-lz4
mariadb-plugin-provider-lzma mariadb-plugin-provider-lzo
mariadb-plugin-provider-snappy mariadb-server mariadb-server-core pv socat
0 aktualisiert, 16 neu installiert, 7 zu entfernen und 1 nicht aktualisiert.
2 nicht vollständig installiert oder entfernt.
Es müssen 18,1 MB an Archiven heruntergeladen werden.
Nach dieser Operation werden 10,6 MB Plattenplatz zusätzlich benutzt.
Möchten Sie fortfahren? [J/n] j

Vorkonfiguration der Pakete ...
(Lese Datenbank ... 322073 Dateien und Verzeichnisse sind derzeit installiert.)
Entfernen von default-mysql-server (1.1.0build1) ...
Entfernen von mysql-server-8.0 (8.0.39-0ubuntu0.24.04.2) ...
Failed to stop mysql.service: Unit mysql.service not loaded.
invoke-rc.d: initscript mysql, action "stop" failed.
dpkg: Fehler beim Bearbeiten des Paketes mysql-server-8.0 (--remove):
»installiertes pre-removal-Skript des Paketes mysql-server-8.0«-Unterprozess gab den Fehlerwert 1 zurück
dpkg: Zu viele Fehler, Abbruch
Failed to stop mysql.service: Unit mysql.service not loaded.
invoke-rc.d: initscript mysql, action "stop" failed.
Failed to preset unit, file "mysql.service": Der Link wurde beschädigt
/usr/bin/deb-systemd-helper: error: systemctl preset failed on mysql.service: No such file or directory
Failed to start mysql.service: Unit mysql.service not found.
invoke-rc.d: initscript mysql, action "start" failed.
Unit mysql.service could not be found.
dpkg: Fehler beim Aufräumen:
»installiertes post-installation-Skript des Paketes mysql-server-8.0«-Unterprozess gab den Fehlerwert 1 zurück
Fehler traten auf beim Bearbeiten von:
mysql-server-8.0
Bearbeitung wurde angehalten, da zu viele Fehler auftraten.
libdvd-pkg: Checking orig.tar integrity...
/usr/src/libdvd-pkg/libdvdcss_1.4.3.orig.tar.bz2: OK
libdvd-pkg: `apt-get check` failed, you may have broken packages. Aborting...
E: Sub-process /usr/bin/dpkg returned an error code (1)

This is really annoying.

There seems to be some trouble with the pre- and post-installation scripts and the mysql.service unit file. But even a forced uninstall (dpkg --force-all --purge mysql-server-8.0) and later re-install does not seem to help ...

What i did now is that I tweaked the /var/lib/dpkg/info/mysql-server-8.0.[postrm|prerm] files and commented the lines trying to stop mysql.service. - As i do not intend to run mqsql-server-8.0 at all, this seems to be the best way achieving the wanted behaviour.

After restarting the machine, I can now log into mariadb, however, connecting from cqrlog does not work yet.

I did on the mysql-console:
ADD USER 'cqrlog'@'localhost' IDENTIFIED BY 'secret password';
and then later tried to import my database dump with
# mysql -ucqrlog -p'secret password' < my-dumped-cqlrlog-db.sql

... however now I get:
ERROR 1045 (28000): Access denied for user 'cqrlog'@'localhost' (using password: YES)

... sorry I am not deep into database stuff ... I just want to have things working.
I already dread, that all the db-syncing stuff between my machines needs to be setup again as well ...

So, how do I set up a nice clean db from the dump in order to make cqrlog run again?

Thanks a lot and VY73
Stefan.