Battery saver on iOS canceling notifications

i’ve noticed that if battery saver is on, iOS devices don’t offer notifications. One of the people that I chat with will not get any notifications until the device is battery saver is turned off. But on that device owing to an ailing battery, it is frequently on.
I’ve noticed this on mine too, but I have less occasion to turn on battery saver.
I know that on android you can disable battery management for certain apps. Is there a way to sidestep this for Delta in iOS?

yip, this is how the battery saver used to work. in “Connectivity” you become aware of that issue pretty directly:

“Low Data Mode” also makes notifications unreliable, btw.

i always wanted to have a warning sign or so in the settings as well (where it now reads “On”), but never came to improving that.

i am not aware of options to exclude some apps from battery saving, let alone triggering that from the app itself.