Thanks everyone for the investigation and fixes coming in. I posted a separate announcement topic for visibility, especially for anyone running their own instance of osm-website.
If anyone is using Rapid or a standalone instance of iD (such as the development preview) and got logged out in the last couple days, the osm-auth breakage has also prevented you from getting to the save screen. For now, you can follow these steps to log back in. (Just note that those steps are normally risky and you shouldn’t do that unless you understand the consequences.)