However, if a government prevents you holding Bitcoin completely, which again I'm not sure they could even do since what's classed as owning Bitcoin when its stored in a cold wallet for instance.
Governments can make knowing certain information illegal, such as classified information or illegal numbers as I linked to above. There's no reason they couldn't make knowing bitcoin private keys or seed phrases illegal too.
I buy bitcoin from a local seller that I know most and have trusty and he already helps many local people who want to buy bitcoin without using an exchange. Does the government know the bitcoin transaction? I doubt that ;P
Maybe. Do you trust the person completely and that he isn't handing over your information to anyone else? Where does he get his bitcoin from? Perhaps he buys it all from a centralized exchange where he KYCed, and so his transactions to you are being traced by blockchain analysis companies. Perhaps the government know he is a bitcoin seller and keep him under watch.
If your government are really out to track down bitcoin users, then there is more to staying anonymous than simply avoiding centralized exchanges.