$db_prefix setting was replaced by variable
$database_prefix in Backdrop's settings.php.
If you want to share the entire database, you'll basically end up with the same site with two different URLs. Sharing all tables in the entire database is not hard to do - you just need to indicate that in sites.php. For example, if settings.php for your main site with URL https://example.com is located in folder sites/example, and you want https://another.com to use the same tables in the same database (that is, use the same settings.php), then sites.php should be configured as follows:
$sites['example.com'] = 'example';
$sites['another.com'] = 'example';
This tells Backdrop to use the settings.php file inside folder sites/example for both URLs.
For more sophisticated sharing, there is the Domain module in D7, which has not been ported to Backdrop (there's a request for porting, but it's a large module).
I believe you may have been looking at this page. You may want to experiment adapting that with $database_prefix - I really don't know if it will work or not. Keep in mind that some D7 tables don't exist in Backdrop anymore, they've been moved to json files.