I I agree with everybody else saying that the email server should not be self-hosted. But I have a specific exception to this rule, which I was keen to try, but I never did this or take this with a pinch of salt.

I do self-host on my services, but at the moment I keep myself hosted email on a public server, not on my home server.

Since I am using a tunnel to access my services from outside, my home server is actually using my public server ip. moving my email self-hosting to my home server would not actually change the front facing IP address of that email server, and no harm would be done to my mail server.

But is it really worth it? Probably not. Since I would still need some kind of backup email server out on the internet for the rare situations where my home server is cut from the internet due to power outage or ISP being down.

You want full reliability for your email server. So your home connection without UPS or backup connection isn't going to cut the cheese fully.

So, I would suggest you don't self-host your email on your home server. You can still self-host your email, but on a public server. Be aware, though, that is a difficult task which will require lots of effort and many months to get it done right and accepted everywhere.