Bluetooth - notification sound on phone

When my Bluetooth is connected to my iPhone 13 and a call comes in, I can hear the call notification sound on the Bluetooth AS WELL as on the phone. That is how I like it! When the Bluetooth is connected and a text message comes in, I can only hear it on the Bluetooth and not on the phone. All message notification settings are on ON. The text messages notification come in fine when I don't have the Bluetooth connected. I would like to receive text message notification sounds on the phone as well as the Bluetooth when the Bluetooth is on. My android (I just switched to iPhone) always gave me notification sounds for everything on both devices simultaneously.