Contacts do not sync between iPhone/iPad/iCloud

Contacts between my iPhone, iPad and iCloud have stopped syncing. I am not sure when this started happening, but it must be a while, so I can't go back and pinpoint the reason (new phone? new iPad?, new Mac?) as they all have been updated in the last 9 months. I started noticing this a couple of months ago and tried a bunch of simple fixes and none worked.

So I did some experiments recently. When I add/delete/modify any contact on the web (icloud.com), the change immediately shows up on both my iPhone and iPad. But when I do the same on either iPhone or iPad, the change or new contact doesn't show up on the other device, nor does it show up in the browser (icloud.com). somehow both iPhone and iPad do not upload changes in the Contacts app. What is weird is that changes in my calendar appear instantly on all three devices, regardless of where they were made/initiated.

I have iPhone Xs, latest generation 11" iPad Pro and MacBook Pro (2018 model). And for the experiment all three devices were at home and on the same Wi-Fi network. Any ideas?