Do you know of an Android app that will do this?

I’ve been using an iPhone for almost 2 years now, but used Android from 2009 to 2023. Tasker was always the standard in powerful automation: https://play.google.com/store/apps/details?id=net.dinglisch.android.taskerm&hl=en_US

It sounds very reasonable to expect Tasker to be able to do this, but you post in the Tasker subreddit and find out for sure.

There is also MacroDroid, which some people find more user-friendly, but a little less powerful. But I always found it to meet my needs: https://play.google.com/store/apps/details?id=com.arlosoft.macrodroid&hl=en_US

Basically, it sounds like you want to capture a notification from a particular app (your email client), which would trigger a send email event. I believe I’ve had similar automations in the past.

Do I understand correctly? Do you only want notification that it rang without content of any possible message?

Good question. We have something through Verizon at my workplace, where if somebody leaves a message, then I will get an email if I’m working from home. Although it doesn’t show if they just call but don’t leave a message. I just always figure that if they can’t be bothered to leave a message, then they’ll have to wait until I’m back in the office. But I don’t know of an app that would do that. That would be kind of cool.