Every developer I've heard talk about the subject says that doing online coop for a game like this (bullet hell/twitch game) is extremely difficult
It is extremely difficult, not to relate to my game again but you'll notice that no projectiles really travel too quickly in it.
Even the things that do travel fast in game you'll notice have a wind up and a really predictable pattern.
It's not fun to have an enemy shoot on the server, then half a second later you see it on your scree only to realize you've already been hit.
There are ways to get around this though, it's definitely doable.
You just need to run a lot of stuff on the client as well, and trust it a lot more.
Edit: If anyone's interested look up rollback netcode, or ggpo. They use it in many fast paced shooters like counterstrike, or in fighting games like skull girls.