Thanks for your reply. I got off the phone with Apple, and I successfully got Logic Pro X version 10.5.1 installed on my Mac running macOS Mojave. I'll explain what I did so that if anyone else is having the same problem, they can attempt to solve it.
First we moved my current version of Logic Pro X to the trash. The App Store recognized that I didn't have it installed, but it still wouldn't download the newest compatible version. It kept saying I needed to be running Catalina (which as I stated above, isn't an option for me). The Apple technician talked to his colleagues and said he wouldn't be able to bypass the app store to send me a different version, but that's when my idea came in.
I had previously downloaded a 10.5.1 trial version of Logic Pro X (which I got from the Internet Archive Wayback Machine, getting the DMG from their backup of Apple's official website dated October 30th, 2020). I installed the trial, and we started it to confirm that it was 10.5.1. It was, and then we went back into the app store. It still showed the download button, as if it wasn't installed, but this time when I clicked it, it gave me the option to download the newest compatible version for macOS Mojave (10.5.1). It began to download and install, and though it took a hot minute to finish, it successfully finished installing the app. When I opened Logic Pro X again, it was still 10.5.1, and it indicated it was no longer a trial version. So needless to say, I successfully upgraded Logic to 10.5.1 for Mojave without needing to upgrade to Catalina. I hope this helps someone else who might need this info!
