I used Settings -> System -> System Update. After downloading the update, it booted to the Playdate logo screen, with the top LED light flashing regularly. After several seconds of this, I got the message that my Playdate had crashed. Pushed A, and it's booted into the Playdate logo screen, top LED flashing about once a second, and it's been hanging there for about two or three minutes.
None of the button combos I know about will take it out of that state. Using a paper clip reset seems to reboot it, but it immediately goes back to the same logo-with-flashing-LED. (I've tried holding the paper clip reset for several seconds, until the screen goes blank, but it immediately boots back into the same state). Not sure how to recover from this one apart from letting the battery die.
For the record: I was running the most recent version, and I had it loaded pretty full of season one game PDXes as of last year. (So it's likely several of those PDXes were running older versions of the SDK).
Another data point: I have it connected to USB and am running the simulator with the 1.2 update, to see if it's printing anything to the console. Nothing in the console, and the Device menu isn't appearing.