The issue you’re describing isn’t about which locks are supported but rather what functionality it is you’re looking for. When Locks are paired with SmartThings they use a device handler to communicate with the lock and a device handler provides the capability for SmartThings to communicate with the locks. The basic SmartThings lock device handler only provides the capability to lock, unlock and allow SmartApps to program the lock remotely. The interface you’re seeing on the screen is the device handler interface which is why you’re only seeing lock and unlock options. If you’re using a custom device handler it allows for an expanded access to lock features like auto lock, privacy modes etc.
The key above is that the device handler provides the capability for SmartApps to program codes which is why you don’t see an interface to add user codes. So the next step for you is to install a lock user management SmartApp which allows you to program codes remotely (and do stuff with the user codes).
SmartThings has with a basic user programming app called SmartLocks that gives you the ability to program “permanent” user codes, i.e. program and it’ll stay until until your delete it. You can install this app from within the SmartThings mobile app by following the instructions in this link.
If you’re looking for a more complete user and lock management app which allows for flexible users like permanent, one time, expire on, scheduled, automatic presence and for creating custom actions when user codes are used, custom notifications etc then you need a custom app like Lock User Management (LUM) and you can find the instructions to install custom apps here (if you have access to RBoy Apps).
Hope that helps clear up the confusion about why you don’t see the lock programming features when a lock is paired with SmartThings and how to install the appropriate app of your choice to manage users.