Wow, what a fun question! To give an English learner a canonical phrase to use, I would absolutely suggest that they say "get married to <somebody>". However, given a lot of progressive changes that we're seeing in English, I wouldn't bat an eye if I heard somebody say "get married with <somebody>", and I personally might even prefer to say it that way. The choice of the word in the adverbial phrase has a lot of subtle implications that are probably up for debate, and that sounds like a fun conversation for people that have more prowess with the language.

Agree to disagree? Since when does a non-native speaker from Türkiye have the right to tell an American how to speak English?

This is incorrect, as an English native speaker both “to” and “with” can be used here.

Sir, I hate to break it to you, but I was born in the southwestern United States, and I have no idea what dictionary you’re talking about. You are incorrect, and you are misrepresenting my language to your learners.