@Wilder Ferney Quintero Vanegas
Might have the same error, but for different reasons ...
MySQL server has gone away
and repository are clues for you.
See /home/x/public_html in the paths which could indicate a shared server with shared DB servers.
Are you on shared hosting?
Typically, those on shared hosting cannot make tweaks to shared DB server.
Even if you have attempted to increase values, system is setup to ignore going over your account maxes.
Gone away is related to MySQL server and I see you have shared:
var max:Allow_pocket: 536000010
Is that from your my.cnf file or some interface you have for the DB for your Moodle?
Default value for MySQL is 16M
https://dev.mysql.com/doc/refman/5.6/en/program-variables.html
Using the mysql client on your moodle server or whatever tool you have to work with DB's, what does the following query show:
mysql> show variables like 'max_allowed_packet';
Fact that you've noticed 1G or below ok but anything over 1G no go - wondering how you know a course backup is over 1G?
In the error it shows repository ...
Make the backup deselecting any link you have in course that goes to
a file from a repository. Those could be videos ... large files.
See what happens.
At this stage ... it's a guessing game.
'spirit of sharing', Ken