Hey there ShatterDaze,
If this is happening on two separate Apple products, do you recall restoring from a backup on the newer product? If so, it's possible the backup contains the issue.
Try checking your notification settings for the app(s) that show banners on screen. You'll want to make sure the banner style is adjusted by taking the steps below:
1. Go to Settings
> Notifications.
2. Choose how you want notifications displayed on the Lock Screen:
• View just the number of notifications: Tap Count.
• View the notifications grouped into stacks by app: Tap Stack.
• View the notifications in a list: Tap List.
When notifications arrive, you can change the layout by pinching the notifications on the Lock Screen.
3. To choose when you want notification previews to appear, tap Show Previews, select an option—Always, When Unlocked, or Never—then tap
at the top left.
Previews can include things like text (from Messages and Mail) and invitation details (from Calendar). You can override this setting for individual apps.
4. Tap an app below Notification Style, then turn Allow Notifications on or off.
If you turn on Allow Notifications, choose when you want the notifications delivered—immediately or in the scheduled notifications summary—and turn Time Sensitive Notifications on or off.
For many apps, you can also set a notification banner style and turn sounds and badges on or off.
For more information: Change notification settings on iPhone - Apple Support
Take care!