What problem does this feature solve?
Make 404 page behave as expected. If the text of the page literally says 404 it's expected that the HTTP status code should be 404.
I ran into this because I was automating some tasks, and I expected that hitting this 404 page would return HTTP 404 but when my test failed it took me a few minutes to realize that the 404 page does not return 404.

What does the proposed API look like?
When SSRing, if we are going to show the 404 page, we should also set the HTTP status code to 404.