It's really hard to prove intent & reasonably convincing evidence will be required here.

Examples of things that would be reasonably convincing:

Someone does a large number of similar but independent queries and finds products of sponsors are recommended more than would be expected based on market share or public sentiment.

OpenAI says something like "ad partners have the opportunity to provide more complete product information, thus the LLM has more to work with and naturally recommends them more."

Examples of things that would not be convincing:

Small-N stuff like a guy gets a sponsored product when logged in but a non-sponsored product when logged out.

A blog post or report about a handful of similar small N experiences.

A single report of a statistical correlation between ad spend and product recommendation that could plausibly be explained by differences in market share or something else.

There is some judgement required & a preponderance of significant correlations without definitive proof may be sufficient to resolve Yes, based on the totality of evidence. For transparency, I'm asking this question because no one else has and I wanted to register my prediction somewhere, so I will trade this. Traders are encouraged to review my resolution history before taking a position. In general, I don't default to resolving No unless there's undisputable proof, but the burden of proof I require is pretty high. My prior is that they will try to walk the line between drawing in advertisers by promising results and not obviously putting a finger on the scale in favor of the advertisers.