Is there an app for the iPhone that will read out loud notifications when they’re received?

If a message is long, Siri announces the sender's name and says only that they sent you a message. You can ask Siri to read the full message, or you can open your iPhone or iPad to read it. In Settings > Notifications > Announce Messages with Siri, you can also manage which contacts Siri reads messages from.

Announce Messages with Siri on AirPods - Apple Support