FYI, Chromium's (and Vivaldi's) cookie and data storage is centered around the profile, and the profile is associated with at least one application Window, and an application Window can only be associated with one, and only one, profile. All tabs in that Window, and tabs in any other Window associated with that profile, are using the same cookie storage.
That is why both the Guest Profile Windows and the Private Window open in separate Windows.
Additionally, even assuming code could (or was) modified to support multiple profiles (or cookie stores) in a Window, that might cause a bit of confusion, especially if the user expects to be able to log in to one website with credentials from a second site. There are quite a few ways that such isolation can go wrong (and probably broken, too).
I'll note that Vivaldi does support a recent standard called "Partitioned cookies", where cookies from a third-party site is only associated with the site referencing them. However, this is something the third-party site have to specifically tell the client, or it will be treated as a normal third-party cookie.
