iMessages don't appear in iCloud
imessage app doesn't appear in icloud
iMac 21.5″, macOS 13.1
Question marked as
You can't see them in iCloud when you have iCloud Messages turned on. They sync via iCloud but cannot be viewed there. Also see the following from Keep your messages up to date with iCloud - Apple Support
You can see them on any device that’s set up for iCloud and Messages, including your iPhone, iPad, iPod touch, and Mac.