Green card seekers must leave U.S. to apply, Trump administration says

Let's saying you're dating somebody on a work visa, if you wanted to marry and sponsor their residency, would they now need to return to their home country to wait for the embassy?

The embassies reviewing applications put a LOT of weight on time spent in person, BUT they also require the US applicant to have domicile. So effectively, the only way to proceed is a long-distance marriage that could take years to process a visa for (remember: move abroad, and you could lose the domicile required to sponsor the green card).

So with our shrinking birthrates, our regularly documented & growing "will never marry" population, immigration effectively cut off, what does the future of this country even look like anymore?

or is it effective all the way back at I-140 time where people would then need to spend years away from the US?

I don't believe that's correct. H1-B is formally a temporary, nonimmigrant work visa/status which permits "dual-intent" (meaning a holder can be openly seeking permanent residence when applying for [or when on] such a visa without that dual intent being immigration fraud).