My 2 cents

I bet it has something to do your vacation. You should have not take one month vacation since your department is so buy. That is too long. In my opinion, 3 weeks is the maximum.
I used to work for a small company and once mentioned about one month vacation with a co-worker. He told me don't do that. If you want to take one month vacation, the company has to find somebody to learn the part you are in charge. The company does not like it.

I doubt you have a case. As an exempt employee, they don't need to pay you overtime.

Just take easy and find another job. Don't burn your bridge.

My two cents