I’m looking to write a plugin that allows you to change the Site Link displayed in the admin screen to a different URL than the WordPress one.
Some context: I have a completely separate UI serving the blog pages instead of WordPress, and want to let bloggers be able to click on the Site Link in the WordPress admin UI to go to that separate UI.
What site link are you referring to? The “Visit Site” link under the blog name in the admin Toolbar? You can add and remove Toolbar menu items with ease. See Class Reference/WP Admin Bar. There are many examples of adding menu items in wp-includes/admin-bar.php.
Even if that is not what you meant, the Toolbar may offer a viable alternative.