AEM Content in edit mode is overlayed by an edit layer, this is why we see rectangles on hover of components with an edit action bar.
It's not advised to customize this behavior, otherwise, you will end up complexing the page editing experience.
Also, Clicking on the link will take the user to a new page, which can be achieved by a simple process (which is OOtB)
- Page#1 - Edit the content, and links
- Page#1 - Click on the Preview mode button -> Page#2 will open
- Page#2 - Click on the Edit mode button to start editing.