How many turns does it take for an unseen servant to pass a healing potion in combat?

Unseen servant reads:

Once on each of your turns as a bonus action, you can mentally command the servant to move up to 15 feet and interact with an object. The servant can perform simple tasks that a human servant could do, such as fetching things, cleaning, mending, folding clothes, lighting fires, serving food, and pouring wine. Once you give the command, the servant performs the task to the best of its ability until it completes the task, then waits for your next command.

Assume I used my bonus action to command it to give the healing potion in my pocket to another character, and that it is within reach when I do. It would take a player one turn to complete the task. A free item interaction to draw the potion, then movement, followed by an action to safely pass it over. But the unseen servant seems to be solely capable of movement then a single item interaction.

How many turns would it take for it to perform this task? And if two or more are necessary what is the order of operations? Can it move after interacting with an object?