Do you think Facebook keeps some kind of quality score at the image/video asset level?

General consensus seems to be that Facebook does preserve a quality score for assets across ad sets and campaigns.

One thing to keep in mind is that the Facebook Quality Score for any given ad creative is determined using 1) the number of times the ad was hidden as well as 2) an assessment of general quality across various dimensions (clickbaitiness, etc.). So it makes sense that Facebook would retain these learnings for a creative across ad sets and campaigns, and doing so isn't difficult.