When ever I play offline the latest version and the identity mod version "link"... in the latest release box the version shows the fabric loader instead of (latest version). and i was confused on how i could fix this

I have fixed it. you go into fabric loader version file and go into notepad. Change Type: release to Type: version and it will change the latest release back into the latest release. Ps: sorry for my jumbled mess of words, i am coming up with the wording as i type :/

This happens when you go offline

it will say Type: release until you change it to Type: version

This isn't related to Identity. If you need to open an issue with Fabric Loader, head over to their GitHub page here. If you need support with Fabric, join the Discord server here and go to #player-support. I don't use the vanilla launcher (I use MultiMC), so I'm not sure how to fix your issue.