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How do you manage those?
Currently I have a waypoint telling me to keep heading through a set of gates. I have no idea what the objective/mission is (I got it at random after being promoted) and I have absolutely zero idea which sector is it pointing to. I could easily jump there.

Also how do I manage currently selected missions. If I chose a mission and it is going to give me a similar waypoint, how do I switch back?
Is this game seriously lacking this basic option of waypoint management?

Check the sidebar, under Personal -> Missions. There you can view briefings on active missions, choose your active mission, enable/disable the guidance.

The mission you got after promotion likely also sent you a message, check the messages log.

PS. Also, if the sector the guidance leads you to is already on your universe map, it will be highlighted, so you could indeed just jump there.