“Confusion about “space” I understand.”
That’s confusing. I take it that you are confused about space. Illustration:
“ The other meaning is that it is topological manifold in which the universe resides and includes all objects of the universe. The latter is the space that still expands or inflated when it was empty.”
To clarify your confusion, distinguish between objects in space and the space in which the objects exist.
”I don’t think “stuff moving apart in space” applies to space of either kind.”
We observe objects in the universe moving apart, not “space expanding.” Objects are “stuff.”
Your confusion is quite apparent in your last paragraph about the “scale factor” of the universe changing and the following:
“ We are kind of measuring around some kind of growing curve rather than in an invariant straight line between faraway objects because our measurement basis includes elapsed time, that is, we are not measuring a distance in the ordinary meaning of the word “distance”.”
You are right to say you can’t explain it well. You are speaking from confusion.
Proper length and distance are real world measurements taken from at rest with (co-moving with) whatever is being measured, i.e., without relativistic distortion of images carried by light and subject to time delay.
Regarding your last sentence, do your own research and explain it to yourself. I’ve been at it all my adult life, now 73.
