As far i can see in your logs. The paths that you say that are missing are regarding the vmware.log that is from the VM Itself. If you login into the vCenter VM using SSH do you have those folders?
If you do not have those folders i would really encourage you to restore a backup or if it is not much trouble to go ahead and install a newly supported vCenter Server. You can upgrade the licenses to install vSphere 6.5 and 6.7 and i also think vSphere 7.
On the other side your ESXi host is compatible with vSphere 6.0 U3 maximum so you will have to still be in version 6.0.
