Assuming your BTCs were bought using a vendor that enforce KYC, few thoughts on:

Bitcoin Transactions

• Bitcoin transactions are, by design, pseudo anonymous, most people does not understand UTXOs management and spend and receive normally from the same address, making, even the pseudo anonymity, very weak.
• Learning to manage your UTXOs is paramount for decent pseudo anonymous privacy, never reusing an address is paramount, most decent wallets nowadays do a good job changing the address every-time you receive, but do a very poor job while spending. Most alt-coiners are so used to address reuse as the norm, so is hard for them to wrap their heads about this important concept.

Bitcoin Mixers

• Many will say that the best way to increase your privacy while transacting with Bitcoin, AFAIK, is mixing with a decent wallet, like Sparrow or Samourai Wallet (with your own node), using whirlpool, you need to understand it and do it right and it is not cheap, best practice is to leave the SATS mixing while you don't need them, once you do, you spend directly from the mixing pool, very clever...

For those thinking people mix or swap for tax evasion

• If you are one of those that thinks this is made for tax evasion, you are still scrapping the surface of cyber security and most probably exposing your self in many other ways to cyber criminals on a daily basis.
• When you pay in cash, Do you attach a ledger with all the transactions you have done before and you balance account? Clearly not. If you use the same address every time, anyone you pay to, can look up your address in the blockchain and check, your balance and every transaction you have done ever.. This, is less than ideal and a big no-no in cyber security, hence, the swaps or the mixing, nothing to do with tax evasion. Any abiding citizen.

Summary:

• Mixers are interesting, but, they can be censored or made illegal, specially if the service is already known to be working with chain analysis companies, others are working on decentralizing further the service, but there are still components that are centralized, making it a no-no for some cyber security savvy people
• A simple swap BTC to XMR to BTC does the job and anyone can wrap their head around it in a minute.
  • The ones that call themselves maximalists argue this is working with "shit coins", for me that is non sense, Monero is excellent tech for privacy and anonymity but not decentralized enough for my liking, therefore, swapping to it and back to Bitcoin seems only logical to me. Some say, use Bitcoin for saving and Monero to spending, I do not agree, I like to use BTC for both, how else will it become the internet of money if all we do is hold it? LN is doing a great job creating adoption for spending with an additional layer of pseudo anonymity.