Open the Settings app on your iPhone
Tap Notifications
Tap Announce Notifications
Turn off Announce Notifications
Or, under Announce Notifications, turn off Messages
Open the Watch app if you use Apple Watch
Tap Notifications
Turn off Announce Notifications if enabled
Open Siri & Search in Settings
Turn off Announce Notifications with Siri if shown
On AirPods, use the force sensor or stem controls to stop playback when messages are announced
Disconnect AirPods from devices where Announce Notifications is enabled