When I open the Project Picker, the Recent Projects list does not contain my current project. Why is this?
Working as designed.
The Recent Projects list is designed to quickly switch between your most recent projects. Listing the Current project would be of little use as the user is already in the current project.
In the example below, the user is in First Project, so it is not listed. If the user navigates to another project, say Defects, then First Project will appear in the list so that it is easily selectable but Defects will not appear because the user just selected that project.