The sword is automagically used at the end of the level 1 cutscene. If you look closely you can the the animation as it slides from the UI right into the pedestal… In fact this is just an optical illusion as I turned it off in the UI and enabled the one in the stone ;)
Nara just wanted to see if the princess’ hair spray contains enough flame protection to withstand the hard trials of level 2. So she made sure it gets properly tested.
And as the theme went: death is only the beginning (of this level)