Is it possible to trigger a scene, routine, and/or mode when a certain lock code is entered using smart locks app?
You can do it by adding WebCoRE to your setup.
Otherwise you would need to use one of the special lock management apps instead of Smart Locks.
If you have access to RBoy Apps this app can do all that and lot more in terms or automation, actions and notifications when using user codes, locks and doors (for locking and unlocking)
Is there a method to trigger routines with specific lock codes with the new Edge drivers?
Depends on your lock make and model. For Schlage locks, there are two drivers that expose code slot name in Routines. Z-Wave Lock PH from @philh30 and Universal Enhanced Lock Driver from @RBoy. The Universal lock driver also supports many other makes and models and exposes both code slot and code slot name for Routines. That driver requires a subscription fee to install and use.
Just to be clear, those drivers are for Schlage Z wave locks. They also make Zigbee locks, but I don’t know if there’s a Driver for those that exposes the lock codes to routines.
The Universal Lock driver is also for Z-Wave locks.