Please note that you can choose to terminate the transaction, but all the details will still be visible on the blockchain. The transaction history cannot be erased. For instance, if you sent me 1 BTC, I can send it back to you from a different address to one of your multiple addresses. This way, the transaction is separated from you, making it difficult for others to identify the coins as yours, except for me. However, even with this method, complete anonymity cannot be guaranteed. Mixing services operate on a similar principle, ensuring that recipients of the coins remain unknown.
Even mixing services cannot always guarantee 100% anonymity, let alone bouncing your Bitcoin from one wallet to another. It might make it a little more complicated and time-consuming, but eventually your transaction will be tracked back to the original address. Mixers also depend on how much fee you're charged and the transaction amount, which is why mixers often recommend withdrawing fungible amounts, such as 0.01, 0.10 BTC, and so on, instead of 0.1523 BTC, because there won't be an abundance of transactions with such a specific amount.
Others suggested P2P exchanges or the decentralized exchange Bisq, but they aren't as convenient as centralized ones. Generally, Bitcoin isn't the ideal coin for anonymity; there are others, such as Dash or Monero.