Sorry, another question about the expansion of the Universe

Many times on these boards, it’s been said that the expansion of the Universe is not applicable or observable at our local scale (i.e. things smaller than the Milky Way and our local cluster of galaxies) since the attractive force of gravity in such systems exceeds the effect of the expansion of space at their scales (e.g. Anne Neville in post # 18 here and by Chronos in post #8 here). Are we not talking about two different things? On the one hand space itself is expanding, while on the other, gravitational attraction causes objects in that space to be moving towards each other, notwithstanding that the space between those objects is expanding. So, I can see that the expansion of space at local scales can’t be observed, but I don’t understand why the dominating effect locally of gravitational attraction means that space still can’t be expanding even at such a local scale (and even if things in that space are moving together).

In other words, is it not the case that space is expanding even at local scales but gravitational attraction is drawing things together at a greater rate than that simultaneously expanding space?

Or, phrased differently yet again, in the absence of expansion of space, would the gravitational attraction between even local objects not appear to be stronger?

Thanks!

(and, as always when I ask these types of questions, i.e. about things that I don’t understand at all, please don’t laugh too hard if I’ve made that readily apparent)

Space is expanding on local scales, too, but it’s not relevant.

Basic answer: You’re right.