I managed to talk to a support person at Adobe, and he says it's a bug which they're trying to fix. In the meantime, he gave me a workaround (see below), which does involve turning off the internet (and turning it on again later). I did what he suggested, and it worked; my InDesign is now functioning as it should.
Our team is working closely with Adobe to resolve this. In the meantime, we have identified a workaround that appears to resolve the issue. Please follow these steps carefully:
Disable the firewall on your system.
Uninstall any VPN or antivirus software temporarily.
Save your file (use Save, Save As, or Save As Copy).
Quit the application completely.
Turn off the internet connection on your computer.
Restart your computer.
Once restarted, open Adobe Illustrator or InDesign without connecting to the internet.
Open any file while still offline.
After the application and file are open, turn on and reconnect the internet to your computer.
This workaround has been effective for most users and should allow you to continue working until a permanent fix is implemented.