Assume the Sapir-Whorf Linguistic Theory is accurate: What languages would be best to learn, to improve one's cognitive functions and/or worldview?

Probably whatever language is most grammatically different from one's own, in order to maximize the amount of adaptation your brain has to do to learn it.

(That said, idk if using an already-questionable theory to ask "what language would make you the smartest?" is the most... tactful topic, despite being asked in good faith. It kind of sets the discussion up for inherently offensive speculation about the relative value of different languages.)

Disclaimer: As noted by @McFin it is important to acknowledge that strong Sapir-Whorf is wholly debunked, and even weak linguistic relativity is questionable. @Jordan117's comment is an important note as well - it could be seen as problematic to ask a question like this, because of some of the inherent racist issues with Sapir-Whorf, so I recommend being careful about asking questions that can be dogwhistles! Last point of disclaimer: my wife is a professor of Speech Language Pathology and one of my best friends is a professor of Linguistics, and we have had a similar conversation together in the past when I had similar questions. They explained the following to me:

Learning a new language can keep your brain healthier. As people age, we tend to do less language learning, but the activity of learning a new language can promote brain health. It keeps you thinking, helps you with memory, and gives you something positive to work on.

The benefits don't really correlate to how different the language is. The important thing is to work on skills, and going from English to Dutch, which are relatively similar, still helps keep you thinking and memorizing and exercising your brain (ie. unfortunately the whole premise of your question doesn't really work). Note that this doesn't touch on the cultural impact at all, just what is mechanically happening in your brain.

Mandarin is really different from English so if you want to learn something difficult and different, Mandarin has some stark differences. The grammar is very different, the language is tonal whereas English is not, and the writing system uses logograms (full word characters) instead of phonograms (letters). It's probably not the most different from English, but it is also spoken by a lot of people. The most different language is hard to quantify, but it is likely something spoken by a very small amount of people. Mandarin is very different, and has a relatively high utility being the native language of about a billion people.

Linguistic Relativity is bunk. (sorry to hammer on this). When I asked something really similar, they countered with "Let's assume that the earth is flat. What are the implications of that?" It can be a fun exercise, but we're not going to learn much.

Edit: I'm side stepping the problematic application of Sapir-Whorf to human languages to instead reflect on how mathematical/programming languages have been helpful historically and personally for changing how I understand problem solving.

Studying math it is interesting to see how the language of math can limit or open up new concepts.

All that is to say, while the Sapir-Whorf theorem is suspect and tenuous at best, in math where vocabulary and grammar is technology, the way that mathematicians view their world is highly dependent on the "languages" they've learned. Someone who has primarily studied PDEs is not going to approach data the same was as someone who spent more time with Topology.

Sorry for the giant ramble. To answer your question directly: I wouldn't recommend a human language to change your world view. Learning any language is going to help exercise your brain, just as solving puzzles will. If someone wanted to learn a way of communicating that will open up their methods of thinking I recommend learning to program. If you already know how to program, learn a programming language in a paradigm you haven't experienced. The book Seven Languages in Seven Weeks: A Pragmatic Guide to Learning Programming Languages is excellent for this.

In that case, you should learn a language that is as different as possible from your own.

I'm not too comfortable with the premise of the question, even though it's being asked in good faith. SW is all but debunked in its strong form, and while there are differences in cognition depending on language, they are small and ultimately not so useful (the goluboy and siniy experiments are interesting, but it'd hardly change your life to distinguish shades of blue a split second faster).

That said, to engage with the question at its basic premise: you would need to research in a comparative sense which languages contain the most features that your first language(s) does not. For instance, if English is your first language, perhaps skip over anything with a Latin or Germanic influence, and look to Africa and Asia. Mandarin Chinese might be a good option for its use of tones. Japanese and Korean are also good options for their different sentence construction and agglutinative morphosyntax.

You could also look for what would increase your ability to perceive and produce different phonemes to those already in your own linguistic inventory. It has been shown that babies just a few weeks old can differentiate the sounds that are part of their dominant language from those that are not, and we very quickly lose that perception. So perhaps a Sub-Saharan African language which uses a lot of consonants that English does not (although the clicks in many are dying out) would be useful.

Maybe you just want a language that has more words available for ideas covered by only a few words in your first tongue. German could be a good option here, or maybe indigenous languages.

Possibly you could skip a verbal language altogether, and learn to sign. But then of course you would need to pick which sign language, because there are as many sign languages as there are deaf communities.

There will never be one best tongue for this hypothetical premise, because there are so many linguistic features and variety among all the world's languages. Languages are also tied up inextricably with culture. Which dialect of a given language would you opt for? In fact, perhaps just adopting a new dialect of your own language would be the best answer to this question. You would learn not just how to talk slightly differently, but you would come to understand a different way of life, as language (and dialects can be considered different languages) is impossible to fully extract from the culture that uses it. People who belong to minority ethnic groups in their countries, or are queer, or working class, or are women... All have different linguistic proclivities and perspectives which inform their use of language, and their desire to signal membership of their social circle.

So it might considered a cop-out answer to your question, but I would argue that the best language you can learn is the language that the people in your community that are the most different from you, use. It will broaden your horizons and change your perceptions more completely than will learning a foreign language that you don't have consistent and regular opportunities to speak.