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Make sure that you are including Joomla's configuration.php file of your site in your backup, the file is named exactly configuration.php (all lowercase) and stored in the root of your site. If you have customised the name or location of this file e.g. by editing Joomla's defines.php file, or if this file merely includes a different file in a different location the restoration script cannot find and read it, therefore it cannot copy over the global configuration information normally stored in that file.

No, the database information is totally irrelevant. 

Let's start from the beginning.

When you start the restoration of the site with ANGIE there's a waiting page. What happens there is that we run an XmlHttpRequest back to ANGIE which tries to load and parse the configuration.php file from the root of your site. If it fails, it loads a copy of the blank values Joomla configuration.php-dist which we ship in ANGIE itself. This is stored in your session.

When you click on Next in the Site Setup page, your database information, a new site key and the options in the Site Setup page are merged with the configuration we had read and stored in the session at the very beginning. The result goes through the same code Joomla uses in Global Configuration to produce a new configuration.php file. This file is the written to disk — or you are told this is its content, paste it yourself, if we can't write it.

What you describe tells me that reading the configuration.php file failed. As a result the blank values configuration.php-dist file was used. This would mean that any of these happened:

• You were too impatient and didn't wait for the initial ANGIE page to load before clicking Next. This means nothing was read into the session and you are starting with a blank configuration.php file.
• The configuration.php file was not backed up or its name is not exactly y configuration.php (character case matters, i.e. configuration.PHP is a different file which can't be read). You said this is not the case.
• The configuration.php file does not exist in the site's root but somewhere else. You said this is not the case.
• The configuration.php contains anything OTHER than just the JConfig class definition, e.g. an include to a different file, some other PHP code etc which would make including it in a PHP context outside Joomla to fail. You said this is not the case.
• The file was unreadable. Check its permissions.
• The file is otherwise corrupt.

How sure are you that the file is being backed up? If you extract the archive in a completely blank directory do you see a configuration.php file BEFORE you run the restoration (before visiting /installation/index.php)? If not, it's not being backed up.

If the file is there I am pretty sure it contains some PHP which makes it fail to load when we try to include it. The most likely cause would be that your host is using a very old PHP version (5.4 or earlier) by default whereas your site is using PHP 7.4. This mismatch could indeed cause the configuration.php file to be impossible to read.

If you could ZIP and attach your original configuration.php file I could help you determine if the file itself has something which prevents it from being read correctly. Attachments are private, even in a public ticket, i.e. only you and us will be able to see them.