So, you're correct, and I actually did not know this when I wrote the post you've replied to.
But the point still stands: regardless of which of icon 2) or 3) you get, it still isn't going to alert you to the issue: both are normal icons. 2) appears during a full charge, since then you are also not charging, but connected to power. That is, regardless of 2) or 3), both icons also appear during a normal, actually charging charge cycle, so neither indicates an issue.
> I'm pretty sure macOS always takes action when the battery is about to die unrelated to the state
As I recall it, it was awfully close. But that's not to say that there wasn't still time, and that the OS couldn't have acted. (I didn't drive it to empty to find out!) So, it could be that I'm wrong on this point.
AFAIK, macOS is aware of three different states: 1) no power connected, 2) connected to power (but not charging), 3) charging battery.
2) is indicated by the black background of the battery charging icon, and 3) is indicated by a white background of the battery charging icon.
In the case where the power source can't deliver enough energy for charging (in your case), it is in state 2); and I'm pretty sure macOS always takes action when the battery is about to die unrelated to the state. It'll backup the RAM when the laptop's battery level is dangerously low and shut off itself, and will be restored later.