iMessage not syncing between iPhone 16 Pro and MacBook

A few days ago I upgraded to an iPhone 16 Pro. My issue is twofold: For one, messages are not syncing between devices, particularly my MacBook. I have iMessage enabled and plenty of iCloud storage (2 TB). Secondly, there were issues with the messages app on my new iPhone: At first, the messages app either crashed upon tapping the app icon or launched and froze, becoming unusable. Also, accessing Settings > Applications > Messages was not possible, because tapping on it would crash the settings app. It fixed itself after I removed and inserted the SIM card multiple times. Messages are still not syncing between my iPhone and MacBook. The messages app on my MacBook displays the last messages I sent and received before switching to the new iPhone. Going to Messages > Settings > iMessage on my MacBook, a progress circle ("loading" icon) appears next to my Apple ID and the sign out button as well as both my phone number and Apple ID Email address is greyed out and can't be clicked, as you can see in the screenshot provided. My system language is set to German and my private information is blacked out, but you should still be able to see the issue.