I think if you can assume some level of trust in your search provider (i.e. through payment - let's get to that in a minute), without which you should probably be looking for a new search engine, then you can trust the search engine to
not optimise results for you. If they tell you they don't, then do, then you likely have deeper-rooted issues with the search engine you use.
On the point about payments, there are some potential approaches to handling this, but they tend to be a bit complex and technical. I"m not sur ethis is really a technical problem though (or at least one where a technical solution is what's needed).
A challenge of taking traditional payments is that the identity of the payer is inherently "linked" (to some extent) to the transaction. You could maybe use a privacy.com type intermediary or similar.
What you could do however, is buy a "kagi voucher" or similar, which would be an RSA-blind-signed token that you generated client-side in JS. You'd send it to the server during the payment transaction, and be given back a signed version of the token, which you unblind client-side, then give a backup copy to the user to save, and set it as a cookie to authenticate payment has been made.
That should, in theory, at least un-link the payment from the user. Ultimately though, a bad actor can still trivially correlate your searches (and payment, if you used same IP or browser fingerprint), and all your searches are linked by a common cookie.
So you decide to create some kind of token fountain, which you can auth to with a blind-signed token, and get 50 "search passes" from. Those could be unique per-search, and just be "bearer tokens" you can use. You'd have to trust that this token fountain doesn't record which search passes were issued to which "blind token".
Ultimately, it feels like this problem then becomes "do you trust your search engine?" - I'm not sure this is a problem that technology needs to solve, as ultimately your search provider is seeing your queries and IP, and most users won't realistically change this. A provider that isn't incentized to act against your interests (i.e. something like Kagi which isn't advertising to you or selling data) seems to address this for most user scenarios.