I do my editing in Vegas Pro 19 on a Windows 11 machine. I save the file and choose "Exit" to close the application, and everything appears in order. However, in examining my system, I find a Vegas process still running and still consuming system resources. This doesn't seem right. What can I do?
Kill it in the Task Manager as it appears you are doing. Another option would be to upgrade to VEGAS Pro 20 and see if you see the same issues there. It is an issue that has been looked at by the developers.
FWIW, if you want to exit Vegas quickly without going through the task manager menus, HOS (Happy Otter Scripts) has a free 'Kill all Vegas' utility in the HOS free tools library.