WhatsApp currently does that i.e. 'Notify contacts' after changing the phone number - https://faq.whatsapp.com/android/account-and-profile/how-to-change-your-phone-number/?lang=en , perhaps other chat apps does that as well because they are the once having the ability to sync and message contacts.

But I don't use WhatsApp or most other real-time communication apps, So this does that solution doesn't work for me and but it should for many.