Any mental illness could be regarded as a type of diversity.

Yes, that's the purpose of the term “neurodivergent”, to destigmatize mental illness. Many mental illnesses can be lived with, in a relatively normal way, and could also benefit from societal awareness, accommodation and integration. Also, they could incur a risk of discrimination. They also have no cure, just like a physical disability e.g. a leg amputation, is simply a different body condition that will not change. Much like “person with disability”, the correct term should be “neurodivergent person” or “person with neurodivergency”, to avoid the misappropriation of the word as a derogatory term.

The “all brains are unique” side, doesn't actually work. It's a slippery slope that runs the risk of rendering oppressed minorities invisible. See the, “we are all sexually diverse”, dog whistle that was used in right wing rhetoric as an attempt to erase LGBTQ+ pride.