Haha. Neither was I until very recently. I really had no idea such rigorous research had already been done.
I just figured the extent of it was "Well we can't prove they aren't just communicating unlike we can for say dogs"
By the way, if you'd like an overview of the tests performed, you can read them here.
https://www.researchgate.net/publication/342706263_Language_...
Yes I know it's not proof they use language naturally but this is where that "not being able to prove" thing come into play.
As far we can see, it does look like they use language.
1. We can tell they give each other unique names
https://www.scientificamerican.com/article/dolphins-whistle-...
2. similar use of "baby talk" in mothers.
https://www.science.org/content/article/dolphin-moms-use-bab...
3. Their clicks and whistles three key linguistic laws of efficient communication, namely, Zipf’s rank-frequency law (humpback whales also shown to follow this), the law of brevity and Menzerath-Altmann law...but only till babies reach a certain age!
That humpback whales will communicate with fewer vocalizations in the presence of noise but still seem to understand each other
https://theworld.org/stories/2019-06-13/baby-dolphins-babble...
https://www.biorxiv.org/content/10.1101/2023.01.11.523588v1....
All these things paint a pretty clear picture imo. I'm near certain that most? cetaceans use language.