Android 12 by default combines the Mobile data and the Wi-Fi toggle into the Internet toggle, but you can bring the old toggles back into the menu … Strange system icons pull down menu - #13 by AnotherElk
I would like to have further software ideas about this, but I don’t, perhaps others can come up with something.
As for the hardware side …
You could try whether it makes a difference to put the card into the other SIM slot.
If it was me, I would get a new SIM card from my provider for further testing.
You can of course try to check how a different SIM card behaves in your phone, and how the unrecognised SIM card behaves in a different phone. But even if this then looks conclusive and the SIM card doesn’t seem to be the culprit, it could still be the culprit, stranger things have happened. So the only way to really rule out the SIM card would be getting a new one … or finding a software cure.