When it comes to anonymity, then as you mentioned on buying coins from coinbase but in the time that you had sent out those coins in other wallet then it would already be enough
when you are really that mattering on anonymity issues. Platform wont know if that wallet on where the coins sent from is actually owned by you or into other person since
transferring out bitcoin from a custodial wallet wont really be that keen to follow if that one is a payment to other person or would just simply a single transaction to transfer to other wallet.
This is not correct. Coinbase monitor all withdrawals from their exchange and employ advanced blockchain analysis technology to track these coins and the people who bought them. If OP bought from Coinbase and wants privacy, then he absolutely must take action here.
Mixer only use if you want to clean your Bitcoin since you legally bought it from exchange I don't think you still need to do that . You only want is to hide your main address from exchange that you bought your BTC No kyc exchange is enough for that.
This is also not correct. All exchanges, be they KYC or non-KYC, keep logs of deposits, trades, withdrawals, etc., and can be forced at any time to hand that over to governments, law enforcement, three letter agencies, or anyone else who comes knocking or offers to pay. Using exchanges to "mix" coins is probably making your privacy worse, not better. Using real mixers is also for anyone who wants privacy - it has nothing to do with whether the coins were obtained legally or not.
The best advice given in this thread is from ranochigo. If you want to break the link between your coins and your real identity, then you need to use a service which is designed for doing just that, such as ChipMixer to mix your coins, or Wasabi Wallet to CoinJoin them.