Evaluate and implement a method for checking the health of a CouchDB installation

## Summary

Starting with [this](https://couchdb.slack.com/archives/C49LEE7NW/p1659464808156129) Slack discussion, I would like to capture the thoughts from the discussion and talk about ideas to enhance/implement such a "global health-check-system" (gHCS).

In this particular case, the user performed a cluster setup without using the cluster setup endpoint (API or wizard). A load balancer was then placed in front of it, which led to authentication problems since not every node had the same authentication information.

## Desired Behaviour

After installation and configuring CouchDB, a kind of self-test should be carried out in order to discover the most frequently occurring "errors" or "misconfigurations".

## Possible Solution

A health check could be triggered after a start, a configuration change, by a user, at recurring intervals or in other cases. The "Cookie-Monster-Check" method could be such a point at the gHCS, as well as verifying the authentication information for each node or the check for correct node names or whatever should be checked in order to get a system that is as "error-free configured" as possible.

Start by reading the linked Slack discussion and locating the existing “Cookie-Monster-Check” method; no file or test is named in the issue. Review the cluster setup, authentication, and configuration-check entry points, then define the scope and verification for detecting mismatched node authentication and related misconfigurations.

Written by the indexing model from the issue text.