I went to install a site that I'd been working on at the beginning of this year. The site appeared not to be going ahead, so I removed it from my server. At the time of removal, the Joomla version was 4.3.3 with a PHP version of 8.0.
I just got a call from the client that it's now going ahead. So I grabbed the backup and went to reinstall. I got a Kickstart error saying my version was not compatible with PHP8.2 (which is what I'm now running). I downloaded the file from your site which is called kickstart-core-8.0.4.zip and extracted the kickstart.php file. Retried the install and got the same error. According to your site, 8.0.4 should be compatible up to PHP8.3. Is there a wrong version of kickstart.php included in the ZIP file?
To accomplish the reinstall I just downgraded the PHP version for that URL to 8.1 and the kickstart.php version that I had downloaded worked fine so this isn't holding me up.