Android, Notifications, and setting Autostart and Battery Saver

I use notify.notify to send alerts to my Android phone running the home assistant app.

It works, but only if I configure the home assistant to always run in the background by toggling ‘autostart’ to on in android system settings, plus setting the battery saver for the app to ‘none’.

Compare this with the “DS Cam” app for Synology NAS, notifications still come even with DS Cam using the default system settings of “no autostart” and “regular Battery Saver”. I think that means DS Cam isn’t running in the background at all times.

Is this the case with everyone else? If not, could you suggest how notifications could come through even with default battery saver settings?

If yes, I wonder if our respected HA devs will eventually come around to address this behavior.