Does Istikhara concerning a matter that occupies one's mind mean that one's worry has been taken care of, such as someone who performed Istikhara regarding a course to improve their professional skills—does that mean that the worry about their job and livelihood has been taken care of?

Istikhara is a Sunnah for someone who is hesitant between doing something and leaving it, when they do not know what is good for them. The intention behind it is to ask Allah to choose for His servant what is best for him. If a Muslim performs it according to the prescribed manner, Allah will choose for him what is good, open his heart to what has been decreed for him, make him pleased with it, and divert from him anything else.

Therefore, if a Muslim is hesitant about developing his skills or anything else, it is sunnah for him to perform Istikhara, so that Allah may choose for him what is best.