I don't think that quote from the article is disagreeing with you at all. Like you said, we don't have a cohesive definition or test of consciousness, so research like this doesn't say anything about if this is or isn't similar to human consciousness.

I would guess Anthropic included that sentence to make it very clear they're not claiming human-like consciousness, and dampen journalists writing headlines like "Anthropic discovers their AI thinks just like humans and may be conscious".

edit: later in the article they even more explicitly agree with you

> Our experiments don't show Claude can have experiences, or feel things in the way humans do—in fact, it’s unclear whether any scientific experiment could prove this to be true or false