Hmmm.... Interesting.
I handle contacts in the same ways that you do. Propagation between Microsoft Outlook computer app and all the phone apps (e.g. Microsoft 365 and Messaging) works correctly. The mirroring of the phone information back to the computer via Phone Link is where matching of contact names to phone numbers breaks down for me. FWIW I'm using Windows 11 and Android 10.
Glad to hear that it is working "great" for you! ☺️ Fingers crossed that I will someday be able to say the same. 🤞🏻