I'd want to make a vertical shmup, like mainline Touhou games, but instead of a traditional arcade experience, I'd want to make it a series of score attack challenges, time trials, mini stages, pattern trials, and boss scenes all broken up in a way the scene shooters break up content. I'd contextualize them as things happening around Gensokyo and its connected regions, and you're working towards solving an incident by having multiple smaller problems. There'd be multiple characters to select for the scenes, but Global progress is shared, so you can complete it all with your preferred character and not have to repeat content. With incidents happening all over, I'd make it fairly non-linear, but have character locked to a certain region (set of content) until you finish most of it.
Example is have say, Sanae/Aya locked to Youkai Mountain's region completing content until she's done, and then you'd be able to use her in other regions because she's solved what was happening there. You'd be able to swap do different regions anytime to progress on them, so there'd be freedom in how you eventually complete the game.
I'd want to make it fairly beginner-friendly (because think how many times you've seen "I like Touhou, but I'm just not good at shmups"). I wanna aim for something that teaches and eases people into the genre and rewards them for their time spent with things like achievements, or extras like characters, or dialogue scenes (Touhou is known mostly for its characters first and foremost, and it's important to keep that in mind when making something). Also, no micro-dodging projectiles with semi-random speeds and trajectories for hours on end. That should be a lesson, but not the only lesson for the entire game.
The Story is that someone is working behind the scenes to wear out Reimu with multiple smaller incidents (idea is to reintroduce characters who'd have a grudge against her conspiring together), so other characters from all over can work together or solo to solve it. I wanna avoid the weird situation in mainline where every character seems to complete the incident, but it's obviously intended for Reimu to be the one who does it. Having tons of smaller incidents everywhere lets other characters have a chance at being playable without having to center an entire plot onto them, and can give them interactions too.