I receive messages, but not notifications

I missed an important message yesterday because of this. Messages arrive and the message count on the app's icon increments, but I almost never receive any sort of notification on any device, iPhone 13 mini, 9.7" iPad Pro nor Apple Watch 7.

I tested this with the person whose message I missed: while sitting across a table we messaged each other. He received a notification of my message and it then appeared in the Notification Centre of his iPhone 12, while, though I received his message, I got neither notification.

To the best of my ability, all Messages notifications are enabled on my iPhone and iPad (and the watch is set to mirror the iPhone).

I run my watch and sometimes my iPhone, in Silent Mode but I don't think this should affect visual notifications nor messages appearing in Notification Centre. And the problem still persists when Silent Mode is disabled on my iPhone.

I've powered down all devices (including my Mac) at the same time and left them for 30 seconds or so before powering them up again. It made no difference. Any further suggestions?