server: Refine process lifetime management

Define states and use them to properly handle multiple calls to
`start()`, `stop()`, and `exit()`. (Multiple calls to `exit()` can
happen if there is an uncaught exception or signal during shutdown.)

This should also make it easier to add support for cleanly restarting
the server after a shutdown (for tests or via an `/admin` page).

tests/backend/common.js

@@ -50,10 +50,10 @@ exports.init = async function () {
 
   after(async function () {
     webaccess.authnFailureDelayMs = backups.authnFailureDelayMs;
-    await server.stop();
     // Note: This does not unset settings that were added.
     Object.assign(settings, backups.settings);
     log4js.setGlobalLogLevel(logLevel);
+    await server.exit();
   });
 
   return exports.agent;