Bitcoin has a public address that can always be tracked back to an ip address or even to any exchange account, if the investigation is to be carried out properly, an identity will be unveiled.
Let's also not forget that buying Bitcoin isn't anonymous too, those exchanges where you swap your Fiat to Bitcoin all requires some kind of verification, such as driver's license or national identity cards.
Pseudonymous is the right calling word for Bitcoin instead of anonymous.
The first task is avoid any centralized exchange or P2P that will ask KYC, use no KYC P2P e.g. robosats, agoradesk etc or decentralized exchange e.g. Bisq.
Second, use a non custodial wallet, run full node and use Tor to access it, no one will know your IP address.
Third, use Bitcoin mixer that will able to mix your coins and no one can link your old address with your new address.
This is why I feel like it is not really a big deal and we should not go overboard with anonymity if we do not want to. If this is what someone prefers then I could just say kudos and move out of their way and let them do it, but I do believe that it is not needed, it is a way too much and shouldn't be done and should be useless at that point.