There are three main ways you could do it: Coinjoins, lightning, or monero.

Big coinjoins are decent but I think with the better privacy options we have available today they feel kind of outdated. More expensive for relatively weaker obfuscation. And the effectiveness of blinded coordinators not being able to deanonymize users has been called into question lately (Wasabi and Whirlpool. JoinMarket has other problems.)

I think hopping "off-chain", whether that is an L2 or via a different blockchain that is encrypted, is more effective since it wouldn't be obvious to any outside observer that you left and returned to Bitcoins blockchain in the first place. It would just look like any other normal transaction (when in reality it was a swap for something else "off-chain"). Much more difficult, if not impossible, to follow.

With a big coinjoin it is both fairly obvious that 1) it is a coinjoin and 2) that you own some of those inputs/outputs and later could be narrowed down further by mistakes of the other participants of that coinjoin, mistakes you made, and additional metadata

So that leaves Lightning and Monero. Different advantages.

Lightning could work, but depends on how much you're wanting to move around. Successful transactions are inversely related to how much you're sending. Could run into routing problems potentially.

Quick and dirty on the method I would use: BTC -> Monero -> BTC (swap back to BTC in different amounts to different addresses at random times over the course of a few days)

Recommend doing all this p2p using Retoswap or Bisq. Both use Tor by default. Don't use instant exchange websites.

If you want to try Lightning instead you could do pretty much the same method above just use Robosats. Use wrapped invoices when receiving on Lightning (Either with Zeus wallet or lnproxy.org)