saudi scarf

Q: I see many Qaris and imaams wearing a shawl over their shoulders and some use the Saudi scarf and put it over their shoulders. I wanted to ask if this is part of the Sunnah dressing of Muhammad صلى الله عليه وسلم and why do they wear this shawl / scarf?

Q: Is the red Saudi scarf and igaal a sunnat or is it a sunnah of the Saudi dynasty. I know to wear an Imaamah is sunnah mustimirrah, what about a normal khimaar or scarf?