Tea is made in a new tea bowl that is set on an unlacquered wooden stand called 貴人台. Sweets are served on a pedestalled tray called 高杯 (with 懐紙 folded noticeably), and when the tea is ready, the assistant for the host brings the bowl to the personage. When there are two 貴人 as guests, the assistant serves the first bowl to the first 貴人, then brings a second bowl from the preparation room. After the host makes tea in the second bowl, the assistant brings it to the second 貴人. It is a rule to serve tea in an independent bowl in both the case of 濃茶 and 薄茶.
It is the first of the 小習, and while it is against the spirit of 侘び茶, it is useful to learn the importance of consideration for the guest (CQ57). My interpretation is to learn deference by contrast (貴人 🆚 normal person), and then carry that same deference towards everyone.
➡️ This 建水 can either be the same as before, or it can be a different one. As for the 共茶碗, it can be 楽 or something else. Since the 貴人茶碗 is new, it stands above the 一楽二萩三唐津.
➡️ Theoretically, after お仕舞い, it would be the good moment for the 半東 to pick up the 干菓子. However, KM26 thinks, this creates a lot of movement in the room, so you could pick them up after delivering the 道具 for 拝見. Then you keep them by your side on the waiting 畳 (KM26, I think I would have brought them outside and then come back in to wait).
For 薄茶, it's 茶巾-茶巾, 茶筅-茶筅. Also, bow with the 貴人碗 at the door when leaving and entering. Finally, there's 2 times おしまい, once for the 貴人, and once for the servant.
This is a 点前 for serving a nobleman and his attendants. The point is to make a distinction between the nobleman and his attendants, so a separate tea bowl, whisk, 茶巾, sweet container, smoking set etc. are used.
There are some cues when what needs to happen: