Nextcloud version (eg, 12.0.2) : 13.0.4
Operating system and version (eg, Ubuntu 17.04) : [Don’t know how to check this]
Apache or nginx version (eg, Apache 2.4.25) : [Don’t know how to check this]
PHP version (eg, 7.1) : 7.1
What kind of errors are these, some script that can’t be found? Could be that there is a wrong path still somewhere in the database or configuration. Problem with hosted environments is that they are much harder to debug.
If it is too complicated, I personally would try to migrate the whole setup to a local setup (in virtual machine), then do all the upgrades and configuration changes and then migrate it back to your hosting environment. However, that is not the easiest task. If you can do it, you could also move to a more suited environment (v- or dedicated server).