Privacy question

Hi all, forgive me for my ignorance but here is a question:

Lets say i have been stacking some sats the last 5 or so years, always bought from the same exchange, then transferred to the same hot wallet. Some time ago i understood that a hot wallet is not the best idea, created a cold wallet and transferred almost all sats to it.

I am thinking about privacy alot in the past months, anybody with some brains will know that the hot and cold wallet are from the same person, including governements. Is it somehow possible to get those sats „clean“?

For example if i create another cold wallet, transfer some sats to it. If i make a transaction from this new wallet to pay something, can / will this be tracked to me?

I want to avoid stuff like coinmixer because i dont think that sounds safe.