Responding point-by-point:
I’ve read the documentation, but I couldn’t find clear information directly related to my question.
Excellent. As you can probably guess, there are folks who ask for help without first making their best attempt. When someone doesn’t demonstrate how much of an attempt they have made independently, folks like me have a first-reaction to question how far they got on their own.
It’s common that the docs don’t answer every specific question that you’d have. So I am not surprised.
I’m also not surprised that AIs hallucinate. I encounter this very often. (Despite this, they are still very useful!) Basing your expectation on what AIs told you is generally unwise. But–as you did–trying out what they told you to see if it works was a great choice! Sadly it didn’t work out this time.
Since this message is also listed on the following page, I initially did not think the AI tools were misleading me:
Read carefully the disclaimer at the top of the page. That explains why a message you find there may not actually work the way(s) you expect.
Even though this message is documented there, I have not been able to get this command to work in practice in any way. I hope I have made my question/problem clearer now.
Wait, perhaps I have misunderstood! Is “this command” the MAV_CMD_NAV_TAKEOFF command? From the Automatic Takeoff page, I presume (without verifying!) that the NAV_TAKEOFF mission command would correspond to a MAV_CMD_NAV_TAKEOFF command sent to the plane. And of course, that happens in AUTO mode, with the command coming from a mission, and not from pymavlink’s takeoff helper.
It’s an important distinction (to me) whether you’re actually trying to understand the takeoff command (what it does under-the-hood, in what way(s) is that supported by Plane, etc.) or whether you just want help getting SITL to takeoff (which it sounds like you’ve already solved using the TAKEOFF mode, so I’m guessing not this).
And assuming you want to understand the takeoff command, I can keep helping there. What’s your familiarity with source-diving and debugging code to understand the details of what it does?