I admit ... my frustration got the better of me.

@Wayland
It's good to know that it's not a secure thing to run a website, Worpress or not, on a ClearOS box.
Maybe I expected to much from a box that's already EOL anyway.
Thanks for the tips, I will have to look into them and that is going to take a while.

@Patrick
Thanks.
I have manually executed this command and suddenly a backup started and WP updated:

7 scheduled tasks are still overdue, so it only partially worked and it generated some error messages.
I have also used this in crontab so tomorrow I can see if that did the trick.

I don't think I understand the link you send.
I got stuck when they wrote that it's bad advice to follow the given instructions, but not even the given solution was clear to me.
All I could find was a link to this Python script:
gdc-client CentOS 7

Please advice.