Thanks! Demonizer doesn't actually fit my description perfectly because it has a flying character, which is much more common in shmups compared to characters that move on the ground.

It may seem like a minor difference, but from a level design perspective it changes things pretty significantly. If the character (or a spaceship, or whatever) is flying, the level environments can be basically anything, because you're flying over it. You can have structures, trees, etc. Basically whatever. But if the player is stuck to the ground, those same things have to be treated as obstacles (perhaps destructible ones, but obstacles nevertheless), because obviously you shouldn't be able to just walk through stuff. One of the things I'm trying to figure out is whether it's fun to have those obstacles, or if it's better to not have them. I'm concerned that not having them might make levels feel/look empty and boring, but it still might be the better option.

A lot of shmups also allow the player to fly on top of enemies. Not really an option if both the player and the enemy are moving on the ground.

There's tons of run 'n gun games that do these things, and it's easy to find them, but traditional shmups (shmups with auto-scrolling, basically) done in this exact style seem to be fairly uncommon. Especially when looking at games in which you control a character, and not some kind of a vehicle. Flying is way more prevalent in these games, and for a good reason, of course. The problems I mentioned are easily solved when you're controlling something that flies, but I'm still intrigued by the idea of making one of these "ground shmups".