I am able to open the client interface more than once… at least without connecting to a server (I don’t have one to connect to).
I installed the org.nexcloud.Nextcloud flatpak and ran is using the following command:
flatpak run org.nextcloud.Nextcloud.
The setup wizard popped up. I used escape to close both the setup splash and the general settings tab. I then tried to run it again with the same command. I was warned that the app was already running and the general settings tab came back up.
One option for you might be to run ps -ef|grep cloud and find the two pids listed there. I find that if you kill the second pid in the list it will stop the service and you can run the flatpak again to see if the windows come back. This will stop any sync process as well.