Hi, posting this in case nobody previously sorted it and for future reference: I had this issue with MS SQL 2022 today but managed to solve it after uninstalling every mention of SQL in the Installed Apps list by deleting the below regedit keys:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Microsoft SQL Server
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\MSSQLServer
Then went to: HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Microsoft\Windows\CurrentVersion\Uninstall and used CTRL+F to locate "SetupARP.exe" and deleted every key related to MS SQL 2022.
I initially couldn't find some of the SQL keys in the last location so I found and used "BCUninstaller" to double check for me which was successful and SQL no longer appears in my Installed Apps list.
Hope this helps :)