I have recently upgraded to the new Galaxy S23, and have successfully transferred all of my accounts and information to the new phone from my old S20. However, I am only receiving notifications for third party apps like Youtube on my old phone and receiving nothing on my new phone. All notification and account settings on both devices for the apps are identical both in-app and in the device specific settings. I have not found anything online in my brief research of a similar issue or anything further to do to fix this issue.
Thank you for reaching out to us about the issue you're having. We're here to help you in any way possible. Sometimes, when switching devices, if both phones are powered on, incoming messages don't "know" which device to send it to. PLease power off both devices, and after 3 full minutes, power on only your new phone. At that point, have someone send you a message, to test it.