Make no mistake, Mullvad Leta knows what you searched for and who you are.
/Theater/ has no place in privacy.
The right way to do it, short of FHE, is to encrypt the query client side, pass this to the proxy which does not pass the source IP, which passes this to the search engine for decryption. Search results are encrypted and pass thru in the reverse:
Client (encrypts) -> Proxy (passes thru no IP) -> Search engine (receives, decrypts, performs, and encrypts results) -> Proxy passes encrypted blob of results back to user -> Client privately reviews private search results.
Edit: private.sh tried this in the past but unfortunately was shuttered with the end of gigablast.