What I'm finding out is something carried over from Windows 10. Although the basic Windows UI and 4K streams like YouTube work fine, my RX 580 paired with the TCL TV *really* doesn't like that combination. The card wasn't truly meant for 4K use, after all.
EDIT: That may have been a marginal HDMI cable. Swapped it for another one, and the flickering and static has abated. Plus, I'm gradually getting a grip on the scaling weirdness with Sims 4.