What do I do with the purple flowers on my mushroom plant
Is this the mushroom plant you have? Rungia klossii? If so, you will need to put it in a container and bring it inside for the winter. They don't tolerate frost. You can trim it back and treat it like a houseplant for the winter. When the flowers fade, remove them from the plant.
https://www.gardeningknowhow.com/edible/herbs/mushroom-plant/growing-mushroom-herb-plants.htm