Workspaces are not bound to displays in hyprland. This is one major reason I'm using hyprland over niri, where it's not really possible to work around that issue.

Am I wrong?

Every monitor has its own set of workspaces. Workspace 4 on display A is not the same as Workspace 4 on display B is not the same as Workspace 4 on display C.

Functionally you can focus any workspace on any monitor, and ids do not change when doing that. You can set things up both ways, but it's actually easier to just have a key focus workspace x on the current monitor than to lock workspaces to specific monitor.

This is sad. XMonad handles workspaces with multiple monitors exactly the way I want. I really wish other window managers did -- especially on Wayland. Until they do, I'm stuck with XMonad. (Which is good, but it would be fun to get to try something else for once.)

I have been using https://github.com/tmfink/i3-wk-switch on i3 for years and I just noticed the README also lists sway - maybe it helps.

movecurrentworkspacetomonitor will get you to whatever you want to do, just maybe not in a one liner keybind.

There's also focusworkspaceoncurrentmonitor, and anything more complicated can be scripted trivially to be on one keybind.