I don't think people understand how the friendly option may come off. In the context of this situation (we're her superior here, she's been given a lot of responsibility and trust, the pressure is on for her too), in the context of her military background (and Xia Ren likely being family) and her current position, and in the context of this Eastern culture-inspired story, formality is the respectful and expected tone to take. By being formal, we'd be respecting her boundaries, what she's comfortable with and what she knows. That is a better start to friendship in this case because otherwise we'd be throwing her off-balance. She'd see informality as inappropriate, unexpected and would immediately start wondering what we're trying to achieve by acting so informal.
Also being formal doesn't mean being insincere because as has been said before, the Moon has many faces. Ling Qi of course is gonna have to adapt to different political situations in her life and if she starts learning early, so much the better. Just like the Sincere Negotiator skill, LQ can learn how to be true to herself while not showing her full hand.
[X] Keep things formal between you, show her around the Sect and discuss the mission and expectations, perhaps have a spar?