Exactly this. Don't look at the renewal proces, look at its output. It'll work for all certificate sources and catch other potential errors too (eg the webserver reporting success but not presenting the new certificate)
That'll work too. The idea was to put your own infra in place if you really need that, and it's not very hard to do it, even with completely self-hosted stack.
Pushover is $5 once for personal use, ntfy.sh can be completely self-hostable if you prefer.
I have written a small tool which utilizes pushover for these reasons.
You can receive the notifications on your browser/mobile for free afterwards.