Although it is from the previous version, the registry value to be written is incorrect in the Windows version installer.
This is an example of 2020 (24.0).

Path name is wrong.

[HKEYCLASSESROOT\CLSID{38AE003B-0E4B-4EB8-8D21-DB5ECCBD5624}\LocalServer32]
@="C:\\Program Files\\Adobe\\Adobe Illustrator 2020Support Files\\Contents\\Windows\\Illustrator.exe /Automation"

[HKEYCLASSESROOT\CLSID{4A99261F-223B-4980-B746-9960895D74BB}\LocalServer32]
@="C:\\Program Files\\Adobe\\Adobe Illustrator 2020Support Files\\Contents\\Windows\\Illustrator.exe /Automation"

[HKEYCLASSESROOT\CLSID{4EDAE507-552C-4A3D-81ED-853FBF459F6F}\LocalServer32]
@="C:\\Program Files\\Adobe\\Adobe Illustrator 2020\\Adobe Illustrator 2020\\Support Files\\Contents\\Windows\\Illustrator.exe /Automation"

[HKEYCLASSESROOT\CLSID{4F9C4A42-947D-40B0-BB12-266B735321BE}\LocalServer32]
@="C:\\Program Files\\Adobe\\Adobe Illustrator 2020Support Files\\Contents\\Windows\\Illustrator.exe /Automation"

[HKEYCLASSESROOT\CLSID{93A24F08-D70A-42B1-8B1F-5A7FEC495C64}\LocalServer32]
@="C:\\Program Files\\Adobe\\Adobe Illustrator 2020Support Files\\Contents\\Windows\\Illustrator.exe /Automation"

[HKEYCLASSESROOT\CLSID{98C0ECCB-F1BC-4CEF-9A51-B9F06E40C52E}\LocalServer32]
@="C:\\Program Files\\Adobe\\Adobe Illustrator 2020Support Files\\Contents\\Windows\\Illustrator.exe /Automation"

[HKEYCLASSESROOT\CLSID{C7D18CB4-B414-48DC-A59A-CD89C4476007}\LocalServer32]
@="C:\\Program Files\\Adobe\\Adobe Illustrator 2020Support Files\\Contents\\Windows\\Illustrator.exe /Automation"

[HKEYCLASSESROOT\CLSID{C97944EF-40B3-4D40-A3E6-F8F11AC5A3D9}\LocalServer32]
@="C:\\Program Files\\Adobe\\Adobe Illustrator 2020Support Files\\Contents\\Windows\\Illustrator.exe /Automation"

[HKEYCLASSESROOT\CLSID{D8773E95-0FBB-45E2-9755-C929F86CBFBD}\LocalServer32]
@="C:\\Program Files\\Adobe\\Adobe Illustrator 2020Support Files\\Contents\\Windows\\Illustrator.exe /Automation"

[HKEYCLASSESROOT\Adobe.Color Book Library\DefaultIcon]
@="C:\\Program Files\\Common Files\\Adobe\\Shell\\CC.2020.2020\\icons.dll,4294967107"

File is missing.

[HKEYCLASSESROOT\Adobe.Illustrator.idea\DefaultIcon]
@="C:\\Program Files\\Adobe\\Adobe Illustrator 2020\\Support Files\\Contents\\Windows\\idea.ico"