Yes, if you mean this one:
I also replaced the NotificationStyle extension with MelonNotification in the FBDataChanged_blank_2.aia project and the problem persists.
It would really help if you provided a screenshot of your relevant blocks, so we can see what you are trying to do, and where the problem may be.
To get an image of your blocks, right click in the Blocks Editor and select "Download Blocks as Image". You might want to use an image editor to crop etc. if required. Then post it here in the community.
Taifun
Trying to push the limits! Snippets, Tutorials and Extensions from Pura Vida Apps by 
Taifun.
As far as I can see the blocks look correct
My suggestion is to use logcat to probably find out what's going on
Taifun
You could also test your example using the default icon - :ic_dialog_alert, in case your icon image/path is causing an issue
I changed the icon to :ic_dialog_alert but the problem persists. I also tried on other smartphones Samsung A21 and another Xiaomi, with the same Android version, even on these smartphones when I close the app and the "message" node changes, nothing happens until I open the app if it is the app I am developing. While for the example project FBDataChanged_blank_2.aia, if I reopen the app nothing happens, only when I press the START FB Data Process button I receive the notification. So the notification is "enabled" only when the conditions when Screen1.Initialize occur for my app, while for the example app only when Button2.click - when I close the app as already explained nothing happens when the string of the "message" node changes.
Thanks @Taifun now I am on a Mac computer, I read from your topic that SDK Platform-Tools is downloadable for Windows. I will do it as soon as possible.
I have just installed my test version of fbDataChanged with MelonNotification. (The blocks look the same as yours)
This is working as expected, and my device is receiving notifications when I change the message through the firebase console, having closed the app and removed it from recent items, and with the phone "off" / "locked".
I will leave it for a while, just to ensure that the app is really closed.
Please, con you share this modified file AIA with MelonNotification?
I figured out two things. If I close the app by swiping left, the app gets notifications even if it's not in the app list in the multitasking menu. And it works!
While if I close the app by pressing the "X" as in the photo below, I no longer receive notifications. I'm used to closing all the apps in the multitasking menu this way. 
But I have another problem. When I receive notifications, I receive two notifications. 1. Firebase: message and 2. FB Message why? 
Follow photo below.
2 is the service message
1 is the notification
The notifications should still work even if the app is closed.
Mine is still running now after two hours of closing the app.
Can't you hide the service message?
Also, as mentioned, if I close the app from the multitasking menu by swiping left or right, the notifications work and the service message remains. While if I close all the apps from the multitasking menu with the "X", the notifications no longer work and the service message does not remain and closes. Yet when I close the app by swiping left or right, the app closes, in fact when I reopen it goes into "loading" as if it were starting from scratch.
For me, it shows when the process first starts, then goes away, not to be seen again. This might be an Android 15 thing.
What device do you have your app installed on ?
Xiaomi Redmi Note 12 Pro
Android 13 TKQ1.221114.001 (Xiaomi HyperOS)
No, because a foreground service is running in the background
Which means, your app is still active in the foreground
This is not how it should be
Use logcat to find out what happens
For Xiaomi you might have to disable battery optimization, this extension can help
See also https://dontkillmyapp.com
Taifun
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Thanks to @Taifun and @TIMAI2 because with this information you gave me I solved the problem 
. At first I applied some restrictions regarding energy saving. After that I enabled Autostart in background. Also for the service notification that remained permanent I simply had to disable the persistent notifications in the notifications.
Now I have to implement some conditions in the blocks to make sure that only the "message" node is notified because having set up other nodes that do other things for which I am not interested in receiving notifications, currently despite the configuration of the blocks that I sent you before, I continue to receive notifications even from other nodes that are not "message".
I'm taking advantage of this topic to not open another one since my doubt is always about notifications. How can I make it so that when a notification appears if I touch the notification the app opens? I'm not talking about the service notification, but the one that warns me that there has been a change in the Firebase data. Thanks in advance.
It is in here somewhere:
or maybe this:
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Thanks. In the "to notification" instructions just set the intent.
The process is:
- Take the
set MelonNotification1.Intent toblock - Then hook the
call MelonNotification1.CreateIntentblock on the right side.
Fill in the fields, name: enter the name of the screen you want to open (e.g. "Screen1")`
startValue (optional): if you want to pass a value to the screen.
I typed it here, so if anyone needs it they can read it.