Greetings I_Want_You,
It may not be possible to record the video or audio for certain apps when screen recording with your iPhone, and you'll need to reach out to the app developers to confirm the expected behavior. Check out the information in the following article:
Record the screen on your iPhone, iPad, or iPod touch - Apple Support
"Some apps might not allow you to record audio or video. You can't record your screen and use screen mirroring at the same time."
The following article shows how to reach out to an app developer: How to contact an app developer - Apple Support
"Contact the developer of an iOS, iPadOS, or watchOS app
- Open the App Store on your iPhone, iPad, or iPod touch.
- Search for the app, then tap it. If you can't find it, tap the account button
or your photo at the top of the screen, tap Purchased, tap "Not on this [device]," then tap the app. - The app's product page appears. Scroll to the Ratings & Reviews section, then tap App Support. If you don't see App Support, make sure that you're signed in with the correct Apple ID."
Kind regards.