Hi LiorCo,
Thanks for posting in Apple Support Communities. Great troubleshooting so far.
To confirm, are you using Low Power Mode? If you are then this would explain the behavior you see. Review this article for details: Use Low Power Mode to save battery life on your iPhone or iPad - Apple Support
"When Low Power Mode is on, your iPhone or iPad will last longer before you need to charge it, but some features might take longer to update or complete. Also, some tasks might not work until you turn off Low Power Mode, or until you charge your iPhone or iPad to 80% or higher.
Low Power Mode reduces or affects these features:
- 5G (except for video streaming) on iPhone 12 models1
- Auto-Lock (defaults to 30 seconds)
- Display brightness
- Display refresh rate (limited up to 60 Hz) on iPhone and iPad models with ProMotion display2
- Some visual effects
- iCloud Photos (temporarily paused)
- Automatic downloads
- Email fetch
- Background app refresh
When Low Power Mode is on, the battery in the status bar will be yellow. You'll see a yellow battery icon 
and the battery percentage. After you charge your iPhone or iPad to 80% or higher, Low Power Mode automatically turns off."
If that's not the case, when you exit any of these apps, do you quit them from the app switcher? Just making sure since that might prevent apps from running or checking for content as mentioned in Switch apps on your iPhone, iPad, or iPod touch - Apple Support.
Also, if this happens while connected to cellular data, check to make sure these apps are enabled from Settings > Cellular as that will help them refresh. There's great info about this and other cellular settings in View or change cellular data settings on iPhone - Apple Support.
Check to see if you're using Low Data Mode: Use Low Data Mode on your iPhone and iPad - Apple Support
"How to turn on Low Data Mode
You can turn on Low Data mode separately for cellular and Wi-Fi. Your Low Data Mode settings might vary depending on your carrier. Select the type of plan you have below and follow the steps.
LTE/4G Cellular
- Go to Settings and tap Cellular
- Tap Cellular Data Options, then turn on Low Data Mode.
5G Cellular
- Go to Settings and tap Cellular.
- Tap Cellular Data Options, select Data Mode, then turn on Low Data Mode.
Dual SIM
- Go to Settings and tap Cellular or Mobile Data.
- Tap one of your numbers.
- Turn on Low Data Mode.
Wi-Fi
- Go to Settings and tap Wi-Fi.
- Tap the Info button
next to the Wi-Fi network that you're connected to. - Turn on Low Data Mode.
Your Low Data Mode preferences for each Wi-Fi network are kept up to date across all your devices through iCloud.
What to expect in Low Data Mode
Different apps use different ways of reducing data usage in Low Data Mode. In general, here's what you can expect:
- Apps might stop using network data when you're not actively using them.
- Background App Refresh is turned off.
- The quality of streaming content might be reduced.
- Automatic downloads and backups are turned off.
- Services such as iCloud Photos pause updates."
Best regards.
