You can read "Contre la Pensée Unique", of Claude Hagège (linguist at Collège de France) about it. He introduces the concept of "Galapagos effect", where linguistic differences with links and informational bridges lead to more innovation due to diversity of thoughts.
As a sidenote, speaking in your native language is always easier than speaking in english or any other language. If your mother tongue happens to be a language very well suited for science and mathematics, like French is, why speak english? Especially with other french speakers.
So it seems languages might not change how you think, but might be able to emphasize certain aspects of things like you allude to (I believe).
"African time" and its relation to language: https://wireilla.com/physics/ijrap/abstract/10321ijrap01.htm...
Personality modulated by language: https://journals.sagepub.com/doi/abs/10.1177/136700691243889...
Of course, if you, as a dictator, ban the word "sad" and the adjacent synonyms, people won't stop feeling sad. However, it's likely that they won't be able to reflect on what they feel, which in turn will change the way they think. And it's likely that the psychologists of this country will have a much harder time healing their patients or writing papers about depression.
So I'm left to conclude that the parent post saying that thinking in a particular language could lead to insights that wouldn't happen with a native speaker of another language, is not wrong. However it would be wrong to think that the speaker of that other language could not understand that insight, once explained. (Which is not at all what the parent said; I'm just fleshing this out for my own understanding.)
A language that insists a lot on the logical aspect of the sentence, such as French, will lead the speaker to think more logically. A language that makes it easy to create new words, such as German, will help the speaker to create new concepts.
A speaker of a language where time is represented linearly (say, Indo-Europeans), will think differently about it, compared to someone who speaks a language where the concept of time is much more relativistic. There is a plethora of literature regarding “African time” and why westerners have a hard time to understand African's view of punctuality because of this.
The same goes with personality, it's common that people have different personality depending on the language they speak! I'm personally much more polite in English, as the use of conditionals is much easier than in my native language (French). Some languages are also meant to be spoken differently depending on the sex of the speaker - Japanese comes to mind.
Does that mean that some things can't be translated? Not necessarily, but there's always something lost in translation, along with friction. No language is also “Turing complete”, and there's not a pure 100% overlap between every language. For instance, Estonian has no native word for art because of its peasant origins, and had to borrow the German "kunst"!
There's also a “bandwidth” aspect - some languages are slower to convey information, while others are faster. French is one of the fastest, and if you know French top-engineers, you know that they tend to speak FAST on top of this! ;-)
As such, if your mother tongue is a good language to do science (French) in, and you're discussing with a fellow native speaker, it's preferable to speak in it rather than in English. It's also much more comfortable, and the cultural proximity allows for a better work atmosphere and relationships. Which probably leads to better-performing teams as well.
Sacrebleu