> Given the level of snark and off-topicness, I presume you don't actually expect me to answer the question with dozens of different methods.
Dozens of different methods to ... buy crypto? You can keep them.
I would trust something like Kagi more than any crypto exchange to keep my privacy.
You are right that it may not be a good idea to have all your searches tied to your identity, but mixing crypto into that won't help.