How can I save tabs in iTerm 2 so they restore the next time the app is run?
You can Save and Restore Window Arrangement with &#8679; &#8984; S and &#8679; &#8984; R options under the Window screen in iTerm2

You can start the default Arrangement Option to enable are at Preferences -> General -> Startup  -> Open default window arrangement . 

You can add arrangements with the &#8679; &#8984; S and manage them under Preferences -> Arrangements tab .