I am not 100% sure, but I can assume what is going on. It appears that something is causing that warning, but the MainWP Child hides it. This would normally happen if you have the Security Issues fixed, PHP Error reporting to be specific.
Since it happens, when the Child Plugin is disabled, I think that the warning is produced by some other plugin, so it might be good to try to disable all other plugins one-by-one to see which one causes it. (if it’s not a plugin, it could be the theme or even WP Core problem).
Unfortunately it doesn’t solve the solution. And the error ‘Error while sending QUERY packet’ also returned.
When I disabled the MainWP Child Reporting plugin, the error about the Query packet disappeared. However, the site still immediately disconnects on sync.
I took some time to research this problem and I think I know what is going on. As per this article, the error that you get is related to the total number of database requests a website can make. Basically, the server is not ready to send any further database requests.
Are you able to reach out to the host support and see if they are aware of any server-side limitation that could cause this?
If I found right, it could be the max_allowed_packet setting that needs to be increased.