In Advanced alerts I can see that the APM: Application property has a Status variable, but I do not see the same variable in the AppInsight for SQL: Application property type. Is Availability the one to use?
For overall application status of AppInsight applications you would use the "APM: Application" property type and its associated variables. The AppInsight property types are exclusively for AppInsight properties that are not applicable to traditional application templates.
I ended up opening a ticket with support and they confirmed that "Availability" is the property that is equal to "status" on others. It is limited to Critical/Warning though which worries me a bit since I do like having the ability to filter on "Down" events.
In addition to that I simply typed "Down" into the dropdown for Availability and tested successfully. Weird that it works, but it does.
The Advanced Alert Manager does not list all possible values, rather it lists all current values of applications/nodes/components/etc. based on what property type was selected. The fact that "Down" was not listed as an option simply means that none of the property types selected were currently in a "Down" state at that time.