Check your local building codes: in most places in the US, emergency exit doors have to be usable by someone who is blind, a child, or someone who does not read English, “without requiring any special knowledge such as a code.” So a sign posted next to the door lock doesn’t usually meet code. But this does vary from location to location so you just have to check.
As far as door locks to meet your physical description, it’s the middle of the night here and I just happened to be up for a couple of minutes to take some meds. If I think of any more models, I’ll post later today.
And regarding being able to trigger a routine from a specific lock code being used, that’s typically not just something built into the physical device, The rules engine has to be able to use the data that the lock reports.
SharpTools can definitely do this with its paid tier. I’m not sure about other options. 