DESPERATE FOR HELP!! Thought an app was backed up to my iCloud but it wasn't

Hi, so this is a bit of a long one and doesn't directly concern Apple, but I'm so desperate for any help, I figured I'd try here.

To set the stage, I set up Twitter's 2 Step Authentication on my Twitter account about 2/3 weeks ago. I'd never had it prior, but wanted extra security so I set it up. I scanned the code on the Microsoft Authenticator app and entered the one time password I got from Twitter. I knew I was going to be getting a new phone soon, so I made sure to backup the Authenticator app to my iCloud. I assumed it was like every other app and didn't need a special encryption in order to save my account key. I had absolutely NO way of knowing it would need one because I never got a prior warning, nor did I know I'd need to specifically look that information up. I had no idea until it was too late. A few hours ago, I got my new phone (an iPhone 13) and everything went great because I had all of my stuff backed up to my iCloud. The Authenticator app was saved, so I assumed it would still have my account key for my Twitter account saved to it as well. It did NOT. Now I have absolutely NO way of getting into my Twitter account. I do not have any of my backup codes saved, which is my own fault I know, but I just completely forgot to do that. I have no idea what to do next and I'm absolutely terrified I've just lost my Twitter account. I've contacted Twitter Support, I've been on Microsoft forums, but I haven't had much luck with either yet. Because this concerns my iCloud, I thought I'd try here just to see if ANYONE might have an idea of what to do. Please help me if you can.