I'm of course assigning apps to specific spaces. But my browser has to be in all spaces. MacOS still doesn't remember which window is where when the app restarts or the OS reboots.
I’ve been using the Orion Browser a lot recently. Each profile pretends to be its own app as far as I can tell.
You get separated spaces for work and private and links open in the last used window. This might solve your issue of assigning multiple windows to different spaces.