On Android, Google recently took away the ability for us to control your sounds from inside the app (we are currently working on a solution), but for now you need to go to your phone's settings.
From there you need to find Forza then click on 'Notifications.' You will see a list of Notifications, click on the ones you want to turn off sounds for and then press behaviour.
From the pop up select 'Show Silently.' This will ensure the notification still shows but without making a sound.
Here a video of how to do it on Android:
On iOS go to your iPhone's settings, scroll down to find Forza click on it and then press on 'notifications.' From there you will see a toggle which allows you to turn sounds off.
And a video for iOS: