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It looks like you had previously installed Akeeba Backup but you did not uninstall it cleanly. Most likely you just deleted (some of) the component's files and its database tables. Unfortunately, this is NOT how you are supposed to uninstall extensions in Joomla. It leaves database records behind which tell Joomla that the extension is already installed. As a result, Joomla will try to upgrade instead of install the extension next time you try to install its package. However, since the database tables are missing the update process fails.

What you did requires removing the database records from the #__extensions and #__schemas table pertaining to the Akeeba Backup component. Please note that doing so will create orphaned entries in the #__assets table which may cause problems to your site. That's why you should never try to remove Joomla extensions manually.

If you have a backup of your site from before your failed attempt at manual uninstallation now is a good time to restore it. If this is not possible do what I said in the paragraph above having in mind that what you are doing did create a small problem on your site so please, never, EVER try to remove an extension's files and tables instead of uninstalling it through the System, Manage, Extensions page of Joomla.

If you have just upgraded from Joomla 3 you could not have installed Akeeba Backup 9 — it's only installable on Joomla 4.

In this case something is wrong with your configuration.php file. Either your database name ($db) or the database table name prefix ($dbprefix) is wrong, namely there is a discrepancy in the lowercase and uppercase letters.

If this is not the case, something is broken in your database so despite the fact that we include a SQL script which tries to create a database table (and Joomla executes) your database server does not create the table. Therefore the next line in that script which tries to add the default backup profile cannot execute and returns the error you gave me. If this is the case you need to talk to your host. There is nothing you or us can do to fix a broken database (neither of us has the database access level required to do that).