Android Web Notification Enhancements Firefox

[onequest]

Intro
I'm really glad that I've been able to get some web notifications working on my Android device for some web apps that I've installed, it's cool! But, as I've been testing it out I've noticed some areas that could improve the notification expereince for web apps even further. Keep in mind, I'm a UX Designer and while I'm decently tech savvy I probably don't fully understand the technical limitations or constraints yet but I'll share any resources I have found that helped me learn things. I'm simply trying to point out improvements that could made to a system I want to use and enjoy more on my favorite computing device. 
Note: So far, to keep the parameters of my experiment small, I've only tested notifications with the Mastodon web app on my Android device.

Expected Behavior
1. Notifications will be delivered at least as timely as a native app.
2. Notification will display any relevant content such as text, images, or anything else I might want to see. For me so far it's really only been text and I haven't tested if images or other content show.
3. The notification will display the app name and use the app icon/Ravi on
4.Upon tapping the notification it will drop me in to the relevant section of the web app experience (not the Firefox browser).
5. If I don't have notifications for my web app turned on yet, I'd like a prompt to help me set them up so I don't have to dig through the web app to find out how to do it.
Pretty basic, I may have missed something, but basically the notifications match the behavior of other notifications on my device of choice (in this case, Android).

The Problem(s)
While notifications have been delivered as fast as the Mastodon Android app (which I also currently have installed to test) and they show the relevant notification content (again, all I've tested is text content so far), they don't match the other 2 mentioned behaviors. So far, all notifications from my web app appear with the Firefox icon and the app name "Firefox" and when I tap on a notification it sometimes opens in the Firefox browser and sometimes doesn't open at all. But I've never had it open in the installed web app.
UX Stuff: This causes something called "cognitive dissonance" and breaks the flow of the person's experience with the notification. It feels like the app is broken or that the notifications aren't working properly since people expect notifications to function just like their notifications in other apps. THey expect to see the app icon they're familiar with and the app name and to be talked directly to the spot in that app, not in another app.

Outro
Happy to be challenged on any of this if you see it differently, and if you know more about the technical constraints at play, then please share because I'm sure there's plenty I'm missing. Most importantly, if you're a fellow web app enthusiast who also happens to love pocket computers or you just want to see web notifications improved in Firefox for Android, let's get those Kudos up!! If you've noticed other issues with web notifications on Firefox, let's also talk about those here so we can make Firefox the absolute best browser for web notifications! 🤩

Resources That Might Help? 🤷‍♂️
1. https://developer.mozilla.org/en-US/docs/Web/API/Notifications_API/Using_the_Notifications_API#brows...
2. https://developer.mozilla.org/en-US/docs/Web/API/Badging_API
3. https://support.mozilla.org/en-US/kb/push-notifications-firefox#w_how-do-i-add-web-push-to-my-websit...