Status endpoint should confirm database connection is working

We had an outage of the YouTube integration today because an infrastructure change stopped an instance of Via from connecting to its DB. We weren't alerted to the issue immediately because the status endpoint doesn't check the ability to connect to the DB, like the corresponding endpoints in h and lms do.

Start by locating Via's status endpoint and compare its database check with the corresponding endpoints in h and lms. Verify the endpoint detects when Via cannot connect to its database and reports an unhealthy status, then run the existing status or health-check tests if available.

Written by the indexing model from the issue text.