The TTS site currently shows the default cloud.gov pages 404 page (hit something like https://tts.gsa.gov/baaaaaad to see it). There’s a 404 file in the Cloud.gov 11ty template but it didn’t have a permalink until it was updated for 11ty 2.x last month.
To show ya’lls 404 page/template you just need to add permalink: 404.html to the 404 file and Pages will show it for any HTTP 404 result instead of their template. You’d also want to tweak the 404 page a bit probably since it’s pretty barebones (https://tts.gsa.gov/404)
@caleywoods messaged me: