Every time I change activities from my current desktop, my the new activity that I started has a clean desktop with none of my widgets. I've tried looking in Workspace behaviors, but it seems that the only option available is a checkbox saying "show informal tips".

Is there a way I can switch activities while maintaining my desktop widgets?

An Activity is essentially a unique group of widgets, so a new Activity does not inherit the widgets from another one. What you want to use for this is virtual desktops. These all share the same widgets and layout, within each Activity.