it's maybe wise to clean your AU plugin cache before re-installing Logic & check other things before.
- Go to this path /Users/Your_User_Name/Library/Caches/AudioUnitCache and you should find a file named com.apple.audiounits.cache --> Delete it then restart your computer, open Logic and it will re-scan all your plugins.
That can take a while since Logic will be re-scanning all your Plug-ins.
Now for ANA 2, check also this path /Users/Your_User_Name/Library/Application Support/Sonic Academy/ANA 2 and you should find 3 files in there : ANA 2.dat - ANA 2.settings - ANA2.keyfile
Delete ANA 2.settings & overwrite your ANA2.keyfile by the one downloaded from your account.
Please note that each time, we're talking about your User Library on MacOS, not the main Library.
If you can't see your user library which might be hidden, follow this guide .
There's also a ANA 2 manual uninstall guideline on the support page, it might be wise to try to follow this procedure as well.