It would be useful to know what you've tried thus far.
This is what my Notifications I'm Settings looks like.
Also go into Settings … Apps … Choose your App i.e Message's …
It may also be worth putting your phone into Safe Mode.
Put the phone in Safe Mode which disables your downloaded app's but let's your stock app's keep working. If the issues stop then this highlights a downloaded app as the possible issue. Come out of Safe Mode and start deleting your most recent downloaded app's one at a time until it stops. https://www.samsung.com/uk/support/mobile-devices/how-to-start-my-galaxy-device-in-safe-mode/
Current Phone > Samsung Z Fold³ 5G.
@Baker1212 ,Hello, apart from what is indicated by the partner @BandOfBrothers , check these settings that are also important! Hold down the Facebook Messenger icon and you will see iboton.Click in it and you will enter the app settings.
In Mobile data: Allow use of data in the background and Allow use of data in Data saver.
On Battery: Allow background activity.
Clear the cache in Storage.
Good luck, greetings.
I have same issues as well many many other persons at net, S21 simply don’t get messages thought at real time when its in some deep sleep and need to be waked up (screen on) before messages comes thought.
Hope Samsung is fixing this at coming releases as this is shame at high end phones.