After some spelunking of settings I found that this is now in the settings. On the watch, Settings app; or on the phone, Watch app. Tap Accessibility. It’s a new setting under “App Switcher” - “Auto-Select Focused App” with the explanation text saying, “After 1 second of inactivity the App Switcher can automatically open the focused app”.
And now I know that the screen that opens when you double-click the crown is called the App Switcher.
Cumulative summary of known issues and workarounds for macOS 14.4:
In case it hasn’t been mentioned already, my the two displays on my iMac no longer go to sleep after 15 minutes of no usage. This only started after updating to Sonoma 14.4.
Apparently another (obscure) bug has been discovered, this time in tvOS 17.4:
Looks now like Photoshop was what was waking up the computer. I use it so much I normally keep it running all the time. After I shut it down, the random wake-ups stopped. I do seem to recall a recent Photoshop update.