If you have Illustrator installed but the Astute Manager is not recognising it, please ensure that you do not have Illustrator installed on an external drive. Illustrator should never be installed on an external drive and doing so will cause problems.
Please also ensure that you do not have a beta or preview version of Illustrator installed on your machine. We don't release official compatibility with new versions of Illustrator until they have their official release, so if you have a beta or preview version of Illustrator installed, in this case the installer will place the plugins in that version's folder.
To resolve this, open your Astute Manager and, in settings, check that the installer is pointing in the right direction. For example, for Illustrator 2024 it should be: C:\Program Files\Adobe\Adobe Illustrator 2024\Plug-ins
If Illustrator is installed on your machine correctly, please refer to Detecting and adding plugins to new installations of Illustrator.