Oh sorry. I somehow missed this aspect of your comment.
Here's a definition of takeover-capable AI that I like: the AI is capable enough that plausible interventions on known human controlled institutions within a few months no longer suffice to prevent plausible takeover. (Which implies that making the situation clear to the world is substantially less useful and human controlled institutions can no longer as easily get a seat at the table.)
Under this definition, there are basically two relevant conditions:
The AI is capable enough to itself take over autonomously. (In the way you defined it, but also not in a way where intervening on human institutions can still prevent the takeover, so e.g.., the AI just having a rogue deployment within OpenAI doesn't suffice if substantial externally imposed improvements to OpenAI's security and controls would defeat the takeover attempt.)
Or human groups can do a nearly immediate takeover with the AI such that they could then just resist such interventions.