What should a sister do with two pieces of clothing she found by mistake in a bag among her belongings, knowing that they are not Sharia-compliant because they are half-sleeved and very tight? Is it permissible to sell them and donate their price to avoid sin?

Your sister must return the clothes to their owner. Her lack of religiosity does not excuse her, for the clothes might be for her husband or for her to wear inside her home. If she cannot return them, then she should give them to poor Muslims who can benefit from them in a lawful manner.