Not OP, but the way I use macOS Spaces is to differentiate between work and private. I use Chrome for both, so I have some Chrome windows in my work space, and some in my private space. I do similar things for other apps like iTerm. It's an important feature. I once tried having two different browsers for work/private, but it was a chore to manage which browser I opened links in, so I gave up.
My biggest problem with Spaces is that it never remembers which space anything is in. When I reboot, everything is in the wrong space and has to be moved around.
I've been using Choosy.app for easily managing different browsers for work and personal (and testing), and it works great. You set it to your default browser, and then anytime something opens a browser it pops up a picker. Lots of global and per-site configuration options like browser profile selection, private windows, etc.
I have collections of tabs in different windows and I assign those windows to different spaces. Every time I reboot Chrome all windows are assigned to whichever space is active when I launch Chrome.
I seem to recall that Chrome used to remember these assignments, so maybe it's not a macOS problem, but rather a Chrome problem...?
Btw. Zen Browser or Arc have great management of spaces in the browser. You can quickly switch between profiles without unloading them. So you can be even on a call using work space and switch to personal space. This way you don’t need to have separate windows per profile unless you need to see the content of both at the same time.
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.
My biggest problem with Spaces is that it never remembers which space anything is in. When I reboot, everything is in the wrong space and has to be moved around.