The recognizable part of Amanita muscaria is the mushroom?

That's correct! The recognizable part of Amanita muscaria is indeed the mushroom.

It's the fleshy fruiting body of the fungus that emerges from the ground, usually with a bright red cap and white spots. This iconic appearance is what makes Amanita muscaria so easily identifiable.

Keep in mind that while the mushroom is what we recognize, the actual organism, the Amanita muscaria fungus, exists as a network of threads called mycelium beneath the soil.