Support

The Deprecated PHP notices come from a RocketTheme template or extension (it's part of a library which is used in both, so I can't easily tell you which template or extension it comes from).

What you need to do first is disable the error reporting on the site because it may very well just do the trick. Edit the configuration.php file and change the line with $error_reporting to read

public $error_reporting = 'none';

Please also note that you seem to be restoring to a different or upgraded server which uses PHP 8.2. Joomla 3 itself only support up to and including PHP 8.0. It has partial support for PHP 8.1 and absolutely no support for PHP 8.2. Extensions for Joomla 3 may have even lower maximum support PHP versions. Seeing the error messages, it looks like you are using an older version of something RocketTheme-related which does not support PHP 8 at all.

Do remember, Akeeba Backup's restoration script has a massive range of PHP support: from PHP 5.4 which was released on March 1st. 2012 to PHP 8.3 development versions published a couple of days ago. The fact that the restoration script supports PHP versions spanning over 11 years does not mean that the restored site will support the same PHP versions; it's up to the software that was backed up (namely: Joomla and its extensions) to decide which versions of PHP they want to support. We just facilitate the transfer, we cannot magically rewrite all software to be compatible with newer or older PHP versions. Such a task is not just infeasible, it's completely unrealistic.