Where do you add a global bus processor plugin, in stereo out?

I am trying to install a bus processor plugin to manage my output, as for example the softube Bus Processor 670.
Where should I use it, on stereo out ?
Certainly not in control room, but should I create a dedicated group to act as an internal bus and replace with it all my inner Stereo out and then send its output to the Cubase Stereo Out ?
Stereo Out seems to be a special beast in Cubase ?

I wouldn’t call “Stereo Out” special, though it generally is the default output for a stereo project. This behavior can be changed as desired by changing routing.

The “short” answer to your question is that a bus processor to “manage output” needs to be assigned to whatever output you have assigned in routing. You can do it as you suggest, by adding a group and inserting it there, or simply insert it into the output bus you have assigned.

The advantage of inserting it on output versus a group is that you are assured that there are no other groups also assigned to that output. You are also assured that no channels are bypassing the group and routed directly to the output.

As you noted, placing the processor on the Control Room would subsequently operate on the Control Room routing.

Stereo Out is special in the way that it is an output bus. That means it has no sends, no Direct Routing and it always sends its signal to whatever is set up in the Audio Connections dialog.

Other than that it comes down to personal preference whether mastering plugins sit on the output bus channel or a group channel, that is routed to the output bus.

Softube Flow Studio do not see it as a regular track.

I have no Console 1 and ask myself if it sees Cubase Stereo out track ?

It would be so strange if Console 1 can’t manage plugins on Stereo Out.

It also depends on what you are trying to achieve. I assume that the Softube 670 is a Fairchild emulation - so you might want to use it as parallel compression which means you would need need to create a separate Bus and a Send.
Other than that it’s a matter of personal preference like @Johnny_Moneto pointed out.

You are totally right, I used the 670 Fairchild emulation because I got it in a softube mixing/mastering try for some days because I bought a Flow Studio and want to evaluate the 2 flows subscription Softube offers… and realized I never used this kind of mixing plugin which softube include in some ‘Bus mixing’ flows.
I have to admit my lack of experience and knowledge regarding “bus mixing”; my initial thought was to place one of these “flows” on the stereo out. Clearly, if the 670 requires sends, that approach isn’t suitable, and the only solution is to place the flow on one of the buses feeding into the stereo out. In any case, Flow Studio doesn’t “see” the stereo out—even though it appears as a standard track in the project—and doesn’t offer it as an option for hosting a flow.
I’m making progress thanks to all of you—thank you.

I’ve also noticed the limitation that Console 1 doesn’t fully work on Stereo Out for some reason. It’s not an issue for me, as I generally route all my tracks to a ‘Mix Bus’, then route the Mix Bus to a ‘Master Bus’. This allows me to put Console 1 or any of the other Softube bus processors on either bus depending on needs.

As everyone says, there is no ‘correct’ way to go about the final stages of mixing, but I’ve found that having two busses before Stereo Out helps with gain staging.