What statistical test would I use to see if there is a relationship between teachers mbti personality traits and their students standardized test scores?

Interesting question but there is little chance you will get far. There aren't that many teachers who will share their Meyers traits with you and the students test score could be strongly altered by prior treachers in earlier years. What are you hoping to show? I used an interview tool for decades when I interviewed teachers, This tool gave me somewhat of a MBTI profile of the teacher, it was called the Teacher Preceiver. I think Gallop makes it now.

Good thoughts, but no such information. Perhaps you can work on an idea and get a grant to work on a study.

I have never heard of that type of test, but you certainly have an interesting idea. Personality and style of delivery of information have a huge impact on student success.