You could try Jared, which is an iMessage Chat Bot: https://github.com/ZekeSnider/Jared
There's a sample plugin in the repository, yet this requires some Xcode knowledge.
It seems Apple removed the handler because they launched iMessage for Business https://developer.apple.com/business-chat/. If you look into the API, there‘s a „Message received“ handler, ...
Since you didn't mention whether you checked it or not: Go to Settings → Notifications → Phone.
Enable Lock Screen, Enable banners, Notification Centre, badges, Show previews when unlocked (or acc to your preference) etc.
The registration can fail and need to be re-established. Before you contact Apple support, I would open messages on the Mac and sign out of your AppleID.
Sign out of messages with your AppleID
Check the date / time in the Mac in system preferences. Within 60 seconds of reality should be fine, closer is better of course, but it’s not sub second critical.
The only workaround I have found so far is by deleting the conversations with all the suggested contacts.
If you use Signal/Whatsapp to communicate anyway, it is not a big deal. But it is unbelievable that Apple does not allow you to disable this.
Months later, with no better answers in sight, I decided to try deleting my own contact card (where "Daughter"'s number had been used as mine at one point but had since been removed). I'd been trying to be more surgical about the problem and wanted to avoid this big hammer. It solved the problem.
The detailed steps I took are below. Some of the steps ...
I managed to fix this by switching off Messages and FaceTime, removing the SIM, turning off, switching back on, reinserting the SIM and then manually tweaking the Apple Account contacts (removing the manually added number, which was a duplicate once the reinserted SIM was recognised).
I don’t know which of the above steps are necessary and which are ...