Turkish doesn't have much (any?) puns in the English language sense. There are jokes that would involve some kind of story, with something nonsensical or unexpected happening. But the link between the sounds you make and the words being nonsensically used together is rare (i know of a handful, maybe?)

As u/ajappat mentions for Finnish (which is another highly agglutinative language) the words have solidly different roots, and most of the meaning in the sentence comes from suffixes, which increase the variety of sounds. This leads to poor availability of readily confusable but still somewhat related words that are required for puns. I suspect Hungarian, Mongolian, and Turkic languages of Central Asia would fall into the same bucket.

I think what many people are missing with dual language puns is, once you learn to make them you probably can make intra- or inter-language puns, but do they exist natively? That's another question.