Will my sister be sinful for taking a bag of miswak she found lying on the ground at the airport after her return from Umrah, and what is incumbent upon her to do?

What your sister found is considered a Luqatah (lost and found item), and there is no sin in picking it up. If the bundle has value, she must announce it publicly. However, if it is something that its owner would not care about, then she is permitted to take possession of it and benefit from it, based on what was narrated from Jabir ibn Abdullah (may Allah be pleased with them both), that the Messenger of Allah (peace and blessings be upon him) permitted a man to pick up a stick, a whip, a rope, and similar items to benefit from them.