The Status of a Pareveh Dish Baked in a Meat Oven Immediately After Removing the Meat

Hello Rabbi,

I am familiar with the halacha regarding pareveh food in a meat oven and the distinction between ben yomo and not ben yomo.
My question is about a very specific case -
I baked meatballs in the oven and immediately after removing them, I placed a pareveh casserole in the oven. There was no time interval in between, and for the record, I did not even turn off the oven.
Therefore, concerning the steam from the meat, I thought perhaps the casserole is considered meat.

Is the casserole considered meat or in the status of meat? And how long after eating it should one wait before eating dairy?