Add unit test coverage for logic in `watch:` of settings_panel.vue

Description

This is a follow on issue to address the technical debt identified in this thread.

There is no unit test coverage for any of the logic in the watch: section of app/assets/javascripts/pages/projects/shared/permissions/components/settings_panel.vue.

Unit test coverage is needed here because:

• There's a lot of logic here
• It's confusing and its purpose is unclear at first glance
• It has resulted in bugs in the behavior
• We are going to continue to work in this code in the future and we need regression coverage to safely perform the necessary improvements and refactorings.