Reading conflicting information on this one. iOS 9.1, iTunes 12.3.1. When I sync, any apps I have purchased recently do not show up in iTunes. Some things I've read say it's a bug, some say it's by design. If the latter, is there another way that I can manage apps in a similar way (i.e. see the whole list, sort by name/size/date added, etc., view sizes, date added, select which ones I do/don't currently want installed on the device, etc.)?
Transferring apps from iDevice to iTunes is no longer supported with iOS 9, see Can't transfer purchases from iPhone to iTunes in iOS 9 for details. Using iTunes to manage app on your iDevice is still possible though, but you need to download all apps in iTunes to do that. To automate this, set the corresponding option in Preferences->Store.
You could use a different application to manage the apps rather than iTunes. There is Apps Assist for Mac OSX to help manage all the apps. It can show you which apps you have purchased but not downloaded, duplicates and other features.
You can sort by Name, Version, Category or Release Date.