There is code that is executed when the site is first run after an upgrade. This code is in a zipped folder (.zip) under the /CMSSiteUtils/Import
directory in the CMS project. But since you didn't run the full upgrade process against the CMS project and started with a fresh install of v13, you won't have this zip file. You will manually have to copy this file from here:
C:\Program Files (x86)\Kentico\13.0\Upgrade120_130\CMS\CMS\CMSSiteUtils\Import\Upgrade_120_130.zip
to your v13 site in the same location <your project>/CMS/CMSSiteUtils/Import
in the v13 code.
There is another problem as well, you've already upgraded the database so you'll either have to revert it back to v12 and rerun the process again with this file in place or update the data necessary so the code is executed properly on the first start of the CMS after the upgrade.
Once the upgrade is run properly, then it's a matter of dealing with the rest of the items from there.