When you removed/put back /var it changed all the permissions on /var to root only. This is not satisfactory for human use (though it is very secure
). Either you can re-install/upgrade your postfix install, during this install/upgrade correct permissions will be set;
you can go through manually, and redo all the permissions according to your Makefile from compiling Postfix.
Best option IMHO, re-install Postfix. However, this won't be the only thing needing re-installing most likely. You will have other permissions issues on the system, other files need other permissions too...
For this you can decide how to proceed, a re-install might be necessary
However, you might be able to get by with just a postfix re-install/upgrade.
In the future, when you backup/remove directories/files, ensure the permissions are preserved.