This requires some research. I never used a freeze dryer.
You would need separate trays for meat and milk.
Koshering for pesach would depend on how hot the inside of a freeze dryer gets.
The trays definitely need tevilah if they are made from a metal or glass other than aluminum. As well as any other part of the machine that touches the actual food.
My question is, how does the rewarming work? The food is rewarmed gradually in order to extract the liquid from the food. How hot does it get?