With the release of Honkai: Star Rail 1.2 update, Yukong's companion quest called For I Have Touched the Sky is also available in the game that you can complete to get free rewards like Stellar Jades, Trailblaze EXP, Credits, and more. In this mission, you will get to spend time with Yukong and get to know more about her.
The quest takes place in The Xianzhou Luofu, and you will need at least 34 Trailblaze Level to start the quest. However, you will have to unlock it by finishing Trailblaze Mission "Xianzhou Luofu — A Dragon Gallant, Its Ocean Distant" and reading specific Messages at Stargazer Navalia.
If you have done it, here is how you can complete Yukong's companion mission in Honkai Star Rail.
Honkai Star Rail Yukong Companion Mission: How To Unlock & Complete
To start off the quest, you will have to go to the marked location on the map above in Stargazer Navalia. You will get a message from Xikui, and after reading those texts, you will have to go and meet Welt. He will tell you about a crashed starskiff, and you will have to use Cycrane in order to search for the starskiff and victim.
Once done, you will have to rescue the victim by going back to the place where you found her and you will then have to battle against the monsters. Then talk to Qingni (the victim) and Yukong and then battle against the rest of the monsters and complete a series of dialogues.
After that, go to the Palace of Astrum, which is the location marked on the map, and talk to Yukong to accept her gratitude. After completing a series of dialogues, leave the Palance and talk to Qingni and then accompany her to help her clear her mind.
She will then ask you to head to Stargazer Navalia and recover her lost item by using Cycrane. After that, talk to her and then go to the next marked location on the map and ask Jing Yuan about Yukong's past. Have a long chat with him, head back to the Palace of Astrum, and talk to Qingni.
You will then have to chat with Qingni, and she will give you Yukong's Exchange Diary. Read it and talk to Yanming. Complete a long series of dialogues and go back to Welt and talk to him. Go to the next marked location and accompany Qingni to talk with Yukong.
After completing the chat, a cutscene will appear featuring Yukong, and after that, you will have to talk to listen to Qingni and Yukong to complete the quest.