Did a factory reset on my note 8 and lost most of my apps. When I go to the play store to get them back it says they're already installed. When I search for them on my phone there is no trace of them.
Are you looking in your App Drawer? If you're only looking on the homescreen, you probably won't find it there, since you did a factory reset and the homescreens reverted back to the factory state.
Play is a system app - it shouldn't get deleted when you reset, unless the phone came without it and you installed it manually.
As far as the Play store saying that the apps are installed, that's not what it's saying. It's saying that the app has been installed at some time in the past. Tap the button and it will still install. (But Play should still be in the app drawer.) You can always download the .apk file (for Google Play) at https://www.apkmirror.com/apk/google-inc/google-play-store/google-play-store-12-9-12-release/