Why is it wrong? I think it's closer to a checkbox with label, than a real button. If you couldn't see its design, you'd think it behaves just like a checkbox.

Because it doesn't feature a role=checkbox or role=radio here. And as I said above, the better way out is IMO to remove superfluous aria-checked on it than adding another role, when role=button or element with strong semantic with correct ARIA property is already available on child element which is the triggerable element anyways.

The button role is probably misleading for a button that actually acts more like a checkbox.

In T149502#2767547, @Prtksxna wrote:

The button role is probably misleading for a button that actually acts more like a checkbox.

That is not necessary from the specification. [[ https://www.w3.org/TR/wai-aria/states_and_properties#aria-pressed | aria-pressed is sufficient for transforming ]] a button into a toggle button for assistive technology.
But having both attributes might result in errors for screen readers.

Change 352194 had a related patch set uploaded (by VolkerE; owner: VolkerE):
[oojs/ui@master] ToggleButtonWidget: Remove misleading aria-checked attribute

https://gerrit.wikimedia.org/r/352194

Change 352194 merged by jenkins-bot:
[oojs/ui@master] ToggleButtonWidget: Remove misleading aria-checked attribute

https://gerrit.wikimedia.org/r/352194