Hello Dealmn,
Welcome to Apple Support Communities.
We understand that you subscribe to YouTube Premium but unable to minimize the app to play in the background as expected. We are happy to point you in the right direction.
Please use the steps here to contact the developer of YouTube: 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 or iPad.
- 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.
Let us know if you have further questions.
Take care.