I'm trying to learn what is the status of a pareve container AFTER pareve food that had been cooked in a meat pot is warmed in it? Was the status of the pareve container changed? I did search Mi Yodeya and elsewhere online but cannot find this issue addressed.
If the meat pot had not been used within 24 hours prior to cooking the pareve food, the question doesn't even get off the ground.
Assuming the meat pot had been used within 24 hours of heating up the pareve food, the food would then contain ta'am sheini of meat, which means that the flavor of the meat went into the pot, and then from the pot into the pareve food. This food should ideally not be eaten together with dairy, but you wouldn't have to wait after eating it in order to eat dairy. (if either the meat or the pareve food was suspended in water while in the pot, even this prohibition would not be in place).
Once the pareve food has been heated in the pareve container, there is no significance to the taste of meat that may be transferred from the food to the container and you could use it to heat up pareve or dairy food (even if no food was ever suspended in water). This information comes from Tur/Shulchan Aruch Y"D 88-89.