I agree with Sam that if you have the wherewithal to create some kind of “site is down” page then you’d better spend your time making the site just not be down. But maybe you want Adding an offline page when rebuilding.
The two-container install makes for minimum downtime upgrades most of the time. Sometimes building the new container does a migration that crashes the running site. There’s a way around it, but it’s fairly complicated and those updates happen pretty rarely.
You could also re-point your DNS (or have an elastic IP or whatever Digital Ocean calls it) and spin up a droplet/whatever AWS calls it with a web server with your status message in it.