I think bullet heaven works in the sense that you spray the bullets, but it is also a swarm survivor too so I can agree with that as well.
I don’t believe it was the first, but I do believe it was the one that brought the genre to the spotlight. Since Vampire survivors came out the genre has taken off and we’ve seen a great many takes on it which personally, I’ve enjoyed. I find the rather short gameplay nice for fitting into tight schedules and non-commitment gameplay
Oh it’s 100% inspired by TA, I played that game so much as a kid and this one is it’s spiritual successor IMO