Personally, I would like a combination of 1 and 2.
[] Make it something more open, the whole household invited out to the gardens for a celebration of success
On one hand, I like the idea of exalting their awakening as the great achievement it is. We have to remember that these are the childs of prostitutes and the like. Even if they weren't living in such bad condition as Ling Qingge they still must have led a life of hardship and scorn. It has only been a year and a half or less since they were brought to the White Cloud town to serve the Ling clan and now their circumnstances are changing drastically again,
Look at Min Leidi, the poor girl wasn't even accepted in the temples as an apprentince despite her mother's efforts due to her background. Knowing that gives a whole new dimension to her initiative of building a shrine for Zhengui. Her rejection must have been devastating for her.
So I don't want the message to be "and these are your news duties and obligations, work well". I want to genuinely congratulate them and let them bask in their success. Let them recover some of the self-esteem that has been trampled up to now and enjoy the moment and have hope for the future.
[X] Make it a quiet affair, a feast for the successful candidates and their families
On the other hand, this options feels like it would allow Ling Qi to personally interect with Min Leidi face to face (and a bit the others, but mainly Min Leidi). In the big party, Ling Qi would give a speech, congratulate the four kids, mention a bit of their duties ahead and that's it. She isn't going to, can't due to her position as clan head, mingle and chat with them. She has to keep a proper distance.
And that's a shame. I'm not saying Ling Qi tries to be friends with them. But Min Leidi has worked quite hard for the household already. Teaching Biyu to dance and in particular building Zhengui's shrine, no matter how small and mortal it was, shows a fair bit of dedication and will to contribute. Those achievements should have their reward.
As the "first vassal cultivator of the Ling clan" I think she deserves a bit of direct attention. Just some one-on-one conversation where Ling Qi congratulates and encourages her personally, acknowledging her efforts.
The feast just for the three families would allow Ling Qi to have that kind of close conversation while still maintining the atmosphere of celebration and congratulation, which I agree is really important.
So the first option seems like a good balance between "party" and "solemnity".