Please excuse me for not providing a real answer in a top level reply, however, I think your request is fundamentally flawed.

Any proxy or proxy service can examine your egress data. Necessarily, they will be able to see your connections even if perhaps they can’t decrypt all their content. Many would consider this a privacy violation already, making your request technically unsatisfiable.

However, I’m curious to see if in some sense of the word privacy others feel there are proxy services available that can provide it.