Alright, I have a probable answer. I took the watch apart again, and the connector from [guide|143163|Step 4|stepid=289121|new_window=true] wasn't seated properly. 🤦
When I reassembled the watch the first time, I thought that maybe, since they lined up when I put the two halves back together, they would make a firm connection, but they did not. When I took the watch apart again to investigate, the connector was clearly not attached. I reattached it firmly, reassembled the watch, and powered it back on. The watch stays on now, so I'm pretty sure that was the issue.