Thank you once again for your patience and clear explanations. I appreciate it and I understand now how register/unregister works and should be able to apply it correctly by myself from now on.

I followed your instructions and my site uses my own PagesNav now for the sidebar (as tested by making small changes there). Unfortunately, the sorting is still done via ID though, like this:

Item 1: pages/view/586/rrr

Item 2: pages/view/592/sss

Item 3: pages/view/598/ddd

I will play around with the code to see if I can find the reason, but my guess is that you will be faster. ;)

I just wanted to ask you about this )

There is a separate event for this menu.

You can also unregister it in your plugin instead of deactivating the plugin.

'Elgg\Pages\Menus\PagesNav::register' => ['unregister' => true],
'\ColdTrick\PagesTools\Menus\PagesNav::orderPagesNav' => ['unregister' => true],
'\MyPlugin\Pages\Menus\PagesNav::register' => ['priority' => 800],

In future, use 'Developer tools' plugin to inspect ALL same events