Alright, so I found an absolute trainwreck of a solution. All the ways I have tested (sudo, login, openvt, machinectl, systemd-run) don't work because important variables like XDG_SESSION_ID are not created. So probably these methods don't open up a real session or something...?

What I did is to automatically open up a session for the specified user - in this case using getty. Using these code lines, I created a systemd-configuration and booted it up by running systemctl daemon-reload:

{
    printf %s\n \
        "[Service]" \
        "ExecStart=" \
        "ExecStart=-/sbin/agetty -o '-p -f -- \\u' --noclear --autologin $TARGET_USER %I \$TERM"
} | sudo tee "/etc/systemd/system/getty@tty2.service.d/autologin.conf"

sudo systemctl daemon-reload
sudo systemctl restart getty@tty2

source: https://wiki.archlinux.org/title/Getty

After this, the user has a running session and proper environment variables set up. I use pgrep to wait for the expected process to show up:

sessionPid=""

while [ -z "$sessionPid" ]; do
    sessionPid=$(sudo pgrep -t tty2 -u "$TARGET_USER")
done

The environment variables of the process with the PID $sessionPid can then be borrowed to run startplasma-wayland properly as the desired user:

sudo -u "$TARGET_USER" \
    env \
        $(sudo -u "$TARGET_USER" fish -c "cat /proc/$sessionPid/environ | string split0)") \
        /usr/lib/plasma-dbus-run-session-if-needed startplasma-wayland

The fact, that this command would always end up focussing on tty2 after exiting the plasma session, I kind of abused the openvt-command to force the focus to return to the previous tty:

openvt -sw -- \
    sudo -u "$TARGET_USER" \
        env \
            $(sudo -u "$TARGET_USER" fish -c "cat /proc/$sessionPid/environ | string split0)") \
            /usr/lib/plasma-dbus-run-session-if-needed startplasma-wayland

I also did some quirks like using openvt to find an unused tty. If you want to see the whole thing in action - script is here:

https://git.nuth.ch/manuth/PortValhalla/src/commit/a7ba0a907bb8ac415776d415a8de2ada3715ad35/scripts/Common/Software/rclone/main.fish#L16-L80

Thanks for your answer! I am writing a setup script which installs and configures my system automatically. As the creation of rclone configurations requires passwords, I wanted to boot up a Plasma Wayland session (for each user which needs to be created) and prompt them to create the necessary rclone configurations and sign out afterwards.

My current (non functioning) draft of the script looks like this: https://git.nuth.ch/manuth/PortValhalla/src/commit/10701c7a25a0209630c6a39aac61f187103050e6/scripts/Common/Software/rclone/main.fish#L10-L60