Once all the objectives are complete, to finish the mission you must enter the hangar of your mother ship/base by approaching it and press Space when the green message appears over the aiming reticle. Sometimes you will need to move pretty close to see it appearing, sometimes it will show up being a bit mor farther. It can feel a bit random to be honest, but you just need to be near the hangar.

Pressing Space when the text shows up triggers an animation of your ship landing into the hangar using a random camera, either external or the cockpit one, and your only possible action is to navigate through the HUD menus (bottom-left and bottom-right), where it will appear two options: "Go to Debriefing" (that's it, exit the completed mission) and "Refly Mission" (restart it). If somehow you get an external camera and you don't see the hud, pres Enter without touching anything else to use the Debriefing option, or press the Left or Right keys to automatically move back to the cockpit and be able to mess with the HUD menus without risk of errors.

The same applies when you just want to go back to your mother ship to rearm warheads. Once landed, you will see that option in the HUD, as well a new one to go back to combat.

To mess with the "landing" HUD the landing animation doesn't need to complete. You can exit the mission, rearm warheads or go back to combat while it's still landing.