When people discuss shmup level design, they tend to gas up environmental storytelling as an important element which makes shmup levels more interesting. The idea is that people want to feel a sense of place & space when they play these games, and environmental story-telling is a way of accomplishing this. Instead of drifting through empty voids with timer-based spawns, people want fleshed out settings with a history, character, unique visual flair and spatial consistency.
I think people lump in 2 related but distinct concepts together when they discuss this. They're lumping in an attempt to tell a story through environments with an attempt to create a kinaesthetic sensation via movement & a strong sense of space. Conflating these is like conflating character design with attack animations and vfx - they are both attempts to make the abstract more concrete, and they can both be used to characterize, but the latter is made to be felt on an almost physical level, while the former is primarily meant to engage the more conscious parts of our brain. I will call this the Vertigo Factor - how likely is it that a game will cause vertigo with how it uses movement and space.
The more tangible a space feels & the more interesting your movement through it feels, the better. 3D games have a much, much easier time with this because they already have consistent spatial relationships between different objects & the camera without needing to rely on weird perspective tricks. Flying above a city and then diving down to street level won't require any tricks or shortcuts - the games can do it "for real". 3D allows for various camera shenanigans - swinging, spinning, loops, smooth interpolated movement, all kinds of crazy stuff.
Sin & Punishment 1-2, Strania, Eschatos and Raystorm/Raycrisis do an excellent job at this. Just look at how exciting Raystorm's stage 3 is..
That said, even though 3D games excell at this, 2D games have tried to play around with this as well. Stuff like Espgaluda 2's first boss intro, Twinbee Yahho's ocean stage, and RayForce's tower are good 2D examples of this in action.
IMO, shmups should focus on fleshing out their Vertigo Factor, not their environmental storytelling. I want to feel like I'm flying. I want to feel the background move in an intense and dynamic way, matching the craziness going on in the foreground. I want to tilt my head and lean in and out as I play. I want intense combat sequences to be synced up with bursts of background movement and rotation. I want enemy movement to make sense given the background movement. I want the virtual sensation, and whether the sensation's created with a bunch of abstract cubes or a fully fleshed out world doesn't matter all that much - the feel is the point.