1. Checks that all domains can be accessed via HTTP and HTTPS. If not, DNS might have died.
2. Checks that a few known CMS-generated pages contain some phrases they should contain. If not, SQL might have died.
3. Checks that the HTTPS certificate has enough runway left. If not, certbot might have died.
4. Sends a basic email message from my domain to a gmail account. Receives it via IMAP and sends a reply. Then, verifies the reply. This catches a whole bunch of mail-related issues.
5. Checks the free RAM and disk space. Updates an internal "dashboard" page and sends me an email if they are off.
It only took a couple of hours to hack this together and I must say, I get a much better night time sleep ever since.