Dealing with {dead,live}locked applications

This is mostly an application design issue, but maybe there are ways in which Tide can help users to design their application, or provide middleware that can detect/help resolve issues.

There's a few ways an application can get itself {dead,live}locked, e.g. deadlocking while locking multiple mutexes from the application `State`, panicking while holding a mutex such that all future requests instantly error with a `PoisonError`.

A common way to deal with this in todays landscape of service supervisors is to have a "health check" endpoint which verifies whether the service is currently usable, then a supervisor (such as Kubernetes) uses this endpoint to check if an instance of the service should be taken out of rotation and restarted. Tide could potentially provide pieces of a solution like this to make it easier for developers, or include examples of how such an endpoint could be designed to guide developers.

(split off from https://github.com/rustasync/tide/issues/263#issuecomment-496177676)