Session files ... are the date/time stamps on those new files the same as when you logged on after setting the CFG item in config.php ... that means it's working.
What I shared was the command line client query to 'explain' the mdl_sessions table. Explain shows the structure of the table ... column names, etc. just to show you that the column the error reported should exist does indeed exist.
You were using phpmyadmin and viewing the contents of the table .... not the same. I was using command line client viewing the output of 'explain'.
No, you shouldn't edit any table manually unless you really iknow what you are doing. In this case don't think you need to as it's a matter of config ... me thinks.
Rick might have shared the other variable you might need to add to your DB config ...
max_input_vars = 5000
Restoring a backup is a pretty heavy process and could involve lots of variables.
The value for max_allowed_packet you show doesn't have a designator at the end to indicate what the number represents .... example: max_allowed_packet=950M ... the M means Megabytes.
mysql> show variables like 'max_allowed_packet';
+--------------------+-----------+
| Variable_name | Value |
+--------------------+-----------+
| max_allowed_packet | 996147200 |
+--------------------+-----------+
With no designator, think mysql server will assume it's bytes .... so your setting 268 thousand is around 25M. Remember this was recommended to change ***IF*** you saw 'Server has gone away' in the apache server error logs.
If you changed that to a higher value, today and did not restart the mysql service, those settings have not taken affect.
IF one changes config of apache/php/ or MySQL and one needs to restart apache or mysqld.
'spirit of sharing', Ken