I’m curious to know more about this, does this mean the new address will only be affected, or if they decide to send using the previous address link, It still reflects on the new wallet or becomes invalid. If BTC is sent to the old wallet by mistake, what’s happens to it?
One thing you need to understand is bitcoin is not stored on an address but rather on public ledger called the blockchain. As such all your addresses are permanently recorded too on the blockchain. So for example if there is a bitcoin sent to an address, this transaction is recorded and should this same bitcoin been moved to another address the transaction is still recorded, is the old address now render useless? No it is not it can still receive bitcoin just like it was before, will the transaction between the two addresses be visible, yes it will be showing that you send bitcoin from that old address to new the address, so if the new address is attached to your identity then with the blockchain showing the bitcoin from the address is moved to the new one then everyone will know it belongs to you.
The only way you can simply hide the movement of this bitcoin from the old address to the new address is simply by using co-joins or all this mixers, where you sent bitcoin to the mixer and they actually sent back to you from another source, thereby eliminating direct transfer between your two wallets.
What to do about privacy in the first place is simply to use different addresses to receive new bitcoin, do not use one address always as the sender will get to use this to get your privacy and even know the amount such address holds