I have it the other way around. I have all messenger notifications silenced except email. This way when people message me I only see their messages whenever I feel like checking if I got any messages. All importart stuff goes into my email, and I can see the push notification immediately.

If I did this, my notifications would never stop. I get tens, maybe hundreds of thousands of emails every day. Even heavily filtered, I can only afford to check work email a couple times a day. Most that make it past the filters are still ignored and immediately archived.

You mean from random people? Don't post your personal email publicly then. I have masked emails posted publicly and while I do get occasional spam, it's more like 2-3 emails a month.

A day? How on earth did you get in such a situation?