First: AtoM 2.5.x expects MySQL 5.7, while AtoM 2.6 expects MySQL 8.0. Please make sure that you have carefully reviewed the 2.6 installation documentation and updated all relevant dependencies. Note that we also recommend Ubuntu 18.04 and PHP 7.2 for AtoM 2.6!
Looking at the error message, the next thing I would suggest checking would be the SQL modes set in MySQL, and disabling/removing STRICT_TRANS_TABLES if it is enabled. I believe this might be enabled by default in 5.7 and later - however in the MySQL section of the installation docs for 2.6 we recommend setting different default SQL modes. See the bottom half of this section:
If you want to check or change the SQL modes of an installation, the following page might help:
If you're new to using the MySQL command prompt, we have basic instructions on how to access it, and how to find out your MySQL credentials if you don't know them, here:
If this STILL doesn't work, then one thing we could try next is repeating the upgrade process. Make sure you have your SQLdump outside of AtoM before proceeding!
After dropping and recreating the database, but BEFORE loading your backup, we can try to run the tools:purge command-line task. This will flush any data from the db, which can sometimes be useful after multiple installation attempts. Remember, be sure you have a copy of your sqldump outside of AtoM before running this - everything will be deleted!
Now you can reload the sqldump, run the upgrade task, restart services, clear the application cache, re-index, and see if it helps.
Let us know if this helps.