That’s not the case for most social birds. Tits have been proven to have grammar (compositional syntax) and vocabulary, not being emotion-related vocalizations, which puts them above most animals.

https://www.nature.com/articles/ncomms10986 https://sites.psu.edu/lisablogcorner/2023/01/25/what-did-the-bird-say-japanese-tits-language-like-capability/ https://www.science.org/content/article/these-highly-social-birds-can-make-sentences-just-humans https://www.researchgate.net/publication/327046588_Call_combinations_in_birds_and_the_evolution_of_compositional_syntax

This is a bit of a nascent field so we might identify more species with this trait in the oncoming years.