What is the ruling on a Muslim woman working in the embassy of a non-Muslim country located in a Muslim country? And is this considered cooperation with non-Muslims if her work is originally permissible?

There is no objection to a Muslim woman joining the workforce if the nature of the work is permissible and does not aid in anything forbidden or result in evil deeds such as mixing with men (unrelated males) or being alone with them. However, it is well-known that it is highly unlikely for Islamic guidelines to be observed in such places. Therefore, it is preferable for a Muslim woman to avoid working in them. If she is in need, she should seek places free from evil deeds, for if she fears Allah the Almighty, He will make her affairs easy and provide for her: "And whoever fears Allah – He will make for him a way out, and will provide for him from where he does not expect."