Here's what I would do (and have done in the past).
IMPORTANT! Make sure you have noted down the database connection information of your current live site. You WILL need it.
Set your dev site to Site Offline -> Yes in Global Configuration.
Take a backup. Let's call this NEW_SITE_BACKUP.
Set your live site to Site Offline -> Yes in Global Configuration.
Take a backup of the live site. Let's call this OLD_SITE_BACKUP.
Download the OLD_SITE_BACKUP and keep it somewhere safe. It's your insurance policy if things go wrong.
Upload NEW_SITE_BACKUP and kickstart.php into the new site.
Delete all files and folders from the live site, except for the NEW_SITE_BACKUP and kickstart.php.
Run kickstart.php on the new site and go through with the restoration. In the database page remember to select Existing Tables -> Drop Same Prefix. Also remember on that page to enter the database connection information (remember when I told you to make sure you have noted this information down?) including the same database table name prefix you previously had in your live site.
When the restoration is over, log into the new live site, go to Global Configuration and set Site Offline to No. Click on Save & Close.
Key takeaway: when going from Joomla! 3 to 4 (or vice versa) you must delete all files and folders, and use Existing Tables -> Drop Same Prefix (keeping the same database table name prefix) to ensure that all traces of the previous major version of Joomla are wiped out during restoration of the one in your backup archive.
Nicholas K. Dionysopoulos
Lead Developer and Director
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