To be broken down Later™. If this hasn’t been broken down by the time we want to pick it up, create subtasks then.

For hooks in the general ClientHooks class, just move the definition; however, for hooks that already have a dedicated handling class (such as EchoSetupHookHandlers), consider migrating to the new hook container system (T240307).

Five hooks are not registered in unit tests. We are inclined not to repeat this pattern, but to fix the tests so they work with those hooks, and then register the hooks unconditionally (T256253).