What's the music used in the Summer Surprise trailer?
The music in the https://www.youtube.com/watch?v=XYhNzTfP0Og seems to be unique to it, not featured in https://virt.bandcamp.com/album/shantae-half-genie-hero-ost itself, at least from what I can hear.
Or am I wrong?
Sadly, you are wrong indeed: both tracks aren't unique at all.
The second one that plays when they announce the Sophia III transformation is - quite expectedly - taken straight from Blaster Master Zero, the game Sophia comes from in the first place.
The other one is actually a track used in the game. It is called "Remains" and plays inside the Tassel Town tower ... if you return there after the chase scene you get the first time, which obviously uses a different song. Coincidentally... they even show you that very area when the trailer starts. You can see that being played in the game https://youtu.be/yGYjW0fQ2KI?t=275 .
As for WHY you didn't found that music in the OST... you probably checked the wrong OST. You see, some tracks were only included in the Backer Exclusive OST you got with the "soundtrack tier" backing option for the game https://www.kickstarter.com/projects/1236620800/shantae-half-genie-hero ,
DIGITAL SOUNDTRACK! Ah yes, the OST! This epic soundtrack will include all the game's tunes, plus Kickstarter exclusive Bonus Tracks you won't find anywhere else.
... at least until it was uploaded to Youtube (and anyway, it is used in the game).