Does this work/apply also for all the open files which have not been saved anywhere yet?

The session.xml file has all of the tabs including the ones named “new #” where # is a number.

By default, Notepad++ backs up all tabs/files you are working on every 7 seconds into the backup folder.

Look at @Terry-R’s reply to you as that link is to an article both finding your old session.xml file and Notepad++'s backup folder.

Please read (very carefully) one of the FAQ posts here.

Essentially what you are doing is relying on a feature in the wrong way. Over the years there have been numerous posts of unlucky users who have lost ALL their data due to misunderstanding the processes used for this auto-save feature.

If you follow these guidelines your question then becomes irrelevant as the original answer will then apply.

Terry

on the old laptop there should be a file called session.xml either in npp installation directory or under %APPDATA%\notepad++ (depends on how you used/installed npp before)
Copy it to your new laptop, start npp.