I’ve been looking for the same function. That’s how I stumbled upon this post. I messaged apple requesting this feature.
I’m pretty sure the app you are looking for is :
Heart graph when I found it, I made an account here just to let you (and anyone else that stumbles upon this post looking for these features) know about this app.
I bought and used it yesterday. It uses Apple Watch or other Bluetooth monitors. I did have to troubleshoot to get it to synch with my watch, a couple of resets later and it works just fine.
The alarms only work while the app is in a workout. But for anyone else who may be looking for similar features with an all day monitor, this does have a resting workout. One of the reviewers stated they start a new 24 hour session every morning and had used it 24/7 for over a year.
It has threshold alarms you can set if your heart rate goes UNDER a certain bpm as well as over. Other alert features include personalizing your bpm zones with alerts as you hit these zones, so you know where you are without constantly checking your heart rate. There are other features I have yet to try and figure out and use. The main one of course is that the app is meant to graph your heart activity and allow you to save them, compare, make notes, and such.
There is a flat fee for these pro features, $2.99, with the option to support the company for more.
I hope that helps and is what you are looking for.