The following is what Apple Support had me do and it corrected my issues. I have iPhone 11PRO
Let's attempt the following steps. Navigate to Settings > Notifications > Messages and turn off Allow Notifications. Once it's off, navigate to Settings > General > Reset > Reset Network Settings. This also resets Wi-Fi networks and passwords, cellular settings, and VPN and APN settings that you’ve used before. If you're using iCloud Keychain, these settings are also removed from other signed-in devices.
Your iPhone will restart during this specific reset. After it resets, you will need to reconnect to your Wi-Fi network and turn on notifications for Messages again. Test to see if that helps both on Wi-Fi and on your cellular network.