Is it permissible, Islamically, to breastfeed a baby girl in public places when there is an urgent need, while covering the chest and the baby with a nursing cover, knowing the difficulty of expressing milk and avoiding breastfeeding her in public restrooms?

There is no doubt that the more the mother is able to breastfeed her child in a safe place away from people's eyes, the better it is, due to the modesty involved. If she needs to breastfeed him in front of people, there is no harm in that, while being careful to cover up so that people do not see her breast or anything else.