Can you link to the portion of the debate where everyone agreed on what “under the jurisdiction of” means?

The issue was contentious then as it is now. They wouldn’t have spilled so much ink on the topic if it wasn’t. Your link is proving my point.

Sure, I already did explain it. They explicitly said that "not under the jurisdiction" would cover children belonging to Indian tribes, the children of ambassadors, and they discussed the need to be able to expel occupying armies. Someone said "what about the kids of Chinese people" and the sponsors said "yep, if we adopt this language they'll get to be citizens too".

None of it's complicated. You could read this as an 8th grader and have no doubt what they were trying to do.

Most of the discussion was of the form "hey, could we add an exception to exclude even more people from citizenship" and then the sponsors would say something like, "yes, we agree that those people aren't excluded under the current language; that adding extra language could exclude those people; and that we don't want to exclude those people or change the language." And then Congress voted for the language exactly as it was originally proposed.