A problem with Universal Control

So, I have this problem with the Universal Control function between my Macbook Air (M1) and my 4th gen iPad Air. The Mac is running macOS Monterey 12.3.1. and my iPad is on the currently newest 15.4.1. iPadOS.

Of course, I made sure all of the instructions from the official link hold true.

Furthermore, I have reset network settings on both devices. Tried toggling off all the steps, rebooted several times, toggle them back on and still no results.

The problem is that in the "Displays" menu in of MacOS I don't even have a little "display settings" button/option to click on below the Retina Display graphic, as if my Mac doesn't even recognise an additional screen nearby.

I can Airdrop files between my Mac and my iPad just fine, and my Airpods Pro connect to each one seamlessly. I did notice that my Mac doesn't offer me to "pick-up" a Safari tab if I have it open on my iPad though (something that works instantly between my iPhone and my iPad).

Any suggestions what I should do please? Because this is really starting to bother me, I really was anticipating this function.

Thanks in advance!

Aleksandar