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Please delete the folder plugins/quickicon/akeebabackup from your site and install Akeeba Backup, twice in a row, without uninstalling anything before or in between. Did that help?

You first need to delete the folder plugins/quickicon/akeebabackup from your site. After deleting this folder you will be able to log into your site's backend.

You can use an FTP/SFTP client or your hosting provider's file manager to delete that file. What did you use to put your backup archive and kickstart.php on the live site before you started the restoration? Use the same thing :)

Now you should be able to install Akeeba Backup, twice in a row, without uninstalling anything before or in between.

  but now it's says I'm running PHP 5.4.45, which I'm not.

Your site is most definitely running under PHP 5.4.45. This message simply displays the PHP_VERSION constant set by PHP itself when it was compiled. You can see that the same message is printed by Joomla itself – they copied our code after we had successfully used it in production for more than 5 years.

Please do remember that when you look at cPanel the PHP version it reports is the PHP version cPanel itself runs under. This is NOT necessarily the same as the PHP version your site runs under. Your server most likely has multiple PHP versions installed. Your site runs under the server's default PHP version which, in your case, is the obsolete PHP 5.4.45. Hosts tend to choose the oldest PHP version as the default to avoid spending time doing support for clients who migrate old sites that require obsolete versions of PPH to function. I know it's lame but the hosting business model is based on marginal cost savings.

You need to go to your hosting control panel and choose the newer PHP 7.3 version explicitly. In most hosts this is applied by adding some code at the bottom of the .htaccess file (it's either a single AddHandler line or, more rarely, a small <Files> block with a SetHandler line in it).