But how many store data locally as opposed to in a database? Even for stateful applications, if you have the source code, you could put an http listener on it for your target group to ping as a health check and put your data on FSx. If the app became unhealthy, kill the server and bring a new instance up. Have a minimum and maximum of one.

I wouldn’t go that far though. I would probably use something like Consul to do a local health check first and restart the app if it dies and then do the target group/health check as a second level check.