The top set of links "Main Page | About | Help | FAQ | Special pages | Log out" should be converted to something like MediaWiki:CologneBlueTopbar similar to MediaWiki:Sidebar. (And actually as default I would shrink it to "About | Log out").

We shouldn't introduce new pages for menus. If this is needed, a generic mechanism should be added. ( T272624)

The "Printable version | Disclaimers | Privacy policy" at the top could be removed. Printable version is already linked in the left menu (or maybe that one should be removed), and Disclaimers & Privacy policy could be removed to the footer. (And the footer should be editable too. This goes for all skins!)

This is the footer. CologneBlue renders the footer at the top of the page.
The footer can be customized in https://www.mediawiki.org/wiki/Manual:Footer#Customizing_the_built-in_items

Allowing modification of the footer is interest

The "Special pages" section in the left menu of Cologne Blue has a very bizarre link "Bug reports" that goes to Project:Bug_reports. How do you actually set that? mediawiki.org doesn't have any info about a configuration option like $wgBugReportsLink. This set of special pages is also a random set different to other skins. As with the other areas on the page, it would be nice to be able to edit which pages go here.

Cannot reproduce.

The contents of the top set of links are still not configurable; you can, however, modify links' texts and their targets using the about/aboutpage, help/helppage and faq/faqpage messages; link to special pages list has been removed. Main page and login/logout links are immovable right now.

This menu is now configurable via hooks

Example removing menu:

// Use setup after cache hook to register hook after skin hooks have been installed
$wgHooks['SetupAfterCache'][] = function () {
	global $wgHooks;
	$wgHooks['SkinTemplateNavigation::Universal'][] = function ($skin, &$menu) {
		if($skin->getSkinName() === 'cologneblue'  ){
			$menu['cb-syslinks'] = [];
		}
	};
};