Is there a way to manage bugs within Zephyr instead of switching to JIRA for bug/defect management?

The short answer is no: you have to use Jira for managing bugs.  Scale sits within Jira and is utilising Jira for managing bugs (which it is very good at doing 🙂).  When I'm setting up Scale for a new project I usually build a Scale dashboard to report on test execution, and a Jira Kanban board (plus some Jira Filters) to manage bugs.  Adding those as Favourites works very well and means I don't have to 'switch' between systems - I can keep those open as separate tabs in my browser.