

In everyday conversation, mushroom is considered to be a vegetable. Even I would call that a vegetable. But I have never heard anyone (in everyday conversation) calling mushroom a plant.
By the way, strawberries are not technically nuts. They are actually considered an aggregate accessory fruit.
Culinary categories mix biological types all the time - tomato (a fruit), mushroom (a fungus), seaweed (an algae) - yet all are treated as vegetables in cooking.
You’re falling into a logic trap by using an overly narrow definition of ‘vegetable’. A vegetable is best understood as a plant or plant-like food used in savoury dishes - and that includes mushrooms, even though they’re not biologically plants.
Since ‘vegetable’ is a culinary term, not a scientific one, it’s not valid to reverse that and argue that mushrooms must be plants just because they’re vegetables.