There has been no dial in number for CS for over a decade. It was for Tech Support and Billing. Sadly people called it for everything under the sun so IF you could even get through the queue was hours. As cell phones became popular it was also wasted minutes people had to pay for. They changed it to a ticket system with call back and some live chat - before that was phased out during the pandemic.
The ticket system DOES have some automated ticket replies. Yes. They do that when queues are really high. The ticket will get a reply based on key words and the category. For example a ticket about a quest may be considered a game hint which GMs can’t give - so the template will have general info on how to find quest and game details like Wowhead. A tech suppport ticket may get a general TS troubleshooting reply.
Re-opening a ticket if the first auto reply does not help puts it back in queue.
I assume your tickets were in the wrong category, or that the initial auto reply was just plain not related. Putting it in the right category and/or re-opening it would be the next step. Assuming it is something GMs can help with.
The actual chat penalties? THOSE are not automated beyond the Squelch or the in-game warning.
If you don’t believe me, you can have a Blue quote instead.