Hi Jens,
this is strange. Can you please run these two commands to verify that git is included in your system-wide environment?

which git
cat /etc/environment

The path where git is installed should appear in the PATH.

which git
/usr/bin/git
cat /etc/environment
PATH="/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games:/snap/bin"

shutdown -r now