Support

Your actual problem is a few lines above that:

WARNING |20240326 17:27:23|Failed dumping sde_categories from record #0. MySQL error 1194: Table 'sde_categories' is marked as crashed and should be repaired

This tells you that MySQL reports that the sde_categories table is crashed. Since the table is crashed, you get a snowball of errors which ends up with the MySQL connection being dropped, which is the final error reported and the one you saw.

The obvious solution would be to go into phpMyAdmin, select the table, scroll down to the "With Selected:" dropdown and choose Repair.

However, the tables with the sde_ prefix look like they belong to a Joomla! 1.5 or 1.0 installation since I can see the table sde_core_acl_aro which only existed in those ancient Joomla! versions. I actually see plenty of tables which appear to be leftovers of ancient sites, including those with the fac_ prefix.

My recommendation is to exclude all tables which have nothing to do with your site. Go to Akeeba Backup, Control Panel. Click on RegEx Database Exclusion. Click the plus (+) button at the bottom of the (possibly still empty) listing. For the Type select "Exclude this table" and for the Filter Item type in !/^#__/ then click on the save (diskette) button. This instructs Akeeba Backup to just skip over these tables.