On my windows 11 desktop (current version 12.31) I get the message "The update is being downloaded..." but nothing happens except a spinning circle.
Version 12.32 downloaded fine on my widows 7 desktop.
If it works on one machine but not another, it's likely something to do with the machine. My money would be on antivirus blocking the download.
If the update checker has trouble, you can use a web browser to download the same installer. It's linked from the New Releases posts here or from the Downloads area on the main site.
Had the same issue, but it worked on the 2nd attempt. Might have been a temporary server overload since there are probably a lot of people upgrading whenever a new version comes out.