I may not be doing this correctly, but I often need to just stop PLSQL Developer and do something else, then come back to it. It appears that this will demand I save everything in all windows before I can exit. In VS Code, I can just leave and I will more or less get back where I was on restart. This can of course be fragile but basically it is hugely convenient. Can PL/SQL Developer work this same way? My workaround, which is absurd, is to crash the app from Task Manager and hope that the session recovery gets me back to close to where I was. That is just a wee bit inelegant. Am I out to lunch or is this possible?

In PL/SQL Developer 14.0 you can use the Workset feature for this. See chapter 15 in the User's Guide:

15. Worksets
A workset is a set of Program Windows, SQL Windows, Test Windows, Command Windows, Report Windows and Diagram Windows that you are working on. Changes made to these windows are preserved when closing and reopening PL/SQL Developer, even if you have not explicitly saved or compiled these changes. After finalizing your work you can apply the workset, so that changes to the files and database objects are permanently saved.

A workset holds the window contents, sizes and positions. When a workset is reopened later, windows will be restored exactly like they were previously used.

All workset-related functions are accessible from the Workset group on the File ribbon.