How serious is "site is under extreme load, search is disabled, try again later"

That will be triggered when your web requests are coming faster than your server can handle.

For example, if you have 4 unicorns and, on average, need 200ms to fully process a request, your capacity is 20 requests per second.

If, for a moment, you get 40 requests per second, the extra requests will sit in a queue waiting, and that message will be show. Also, you can’t go blindly setting up more unicorns, as the process to fully answer a web request involves a lot of moving parts that should be carefully evaluated.

Discourse gained a lot of those graceful degradation features recently as we work to scale out and handle some crazy level of traffic for the largest Discourse instances on the internet.