From the NY Times: "Given these patterns, it seems obvious that older Americans should be more fearful of Covid than younger Americans. Yet they’re not." To me this should be one sentence, not two. The two sentences express a single thought, so why the period? Have they tossed their own style book?

Hmmm, sounds good to me. But I hate long sentences so I may be biased. I don't think it's against the style manual though, is it?

I'd say it would be ok either way. The full stop seems to me to give a stronger break, as if you have said the first sentence, paused for it to sink in and then said the second one. Gives a better rhetorical effect, I think.

(speaking of long sentences... I have been reading Wind In The Willows with one of my students. I hadn't remembered how long some of the sentences are. There are whole pages which consist of only two sentences! It's quite a struggle for me, never mind for the student.)

I agree with Bob.