I have tried the same test, under Windows 11 Pro 23H2, and again, VA installs quite happily for both the normal and preview versions of Visual Studio 2022.
Can you please look in your %TEMP% directory for any files called "vsix*.log", which should be the installer log files from the VA install. Can you please then send them to me via the email:
including this thread ID or URL in the description, so we can match it up. Hopefully there will be some errors in the logs to explain why this isn't working.