Currently in the Jira New Issue View, you're only allowed to add yourself as a watcher. It isn't possible to add other users as watchers and see the watcher list.
Allow users to add other users as watchers see the Watcher list, as it's possible in the Old Issue View.
It's an existing feature that is used by many customers so it's important to still allow this functionality.
Switch back to The Old issue view on the profile settings' Lab section.