I was looking for this same thing - saving as a Character Preset or as a Support>Figure/Prop Asset only saves the character morphs and textures. Saving as a Scene Subset as recommended above works beautifully, thanks!
Here are a few additions, if you use Smart Content… (I <3 Metadata!)
Go to Render Settings, turn off Constrain Proportions, and set your Dimensions to 910x910.
Frame your character in the render box for your thumbnail.
Save As>Scene Subset
Save your Scene Subset in a good place in your Library to keep it organized - I’m saving mine in My Library>People.
Navigate to your new character in the Content Library.
Click the Active Pane Options over your Content Library (the little Arrow and 4 lines icon in the top corner)
Content DB Editor
Select your file in the top part of the window
Select your file in the lower part of the window also
Click on Type: in the middle of the window - Select Actor>Character
Make sure the Categories tab is selected on the lower part of the window
Right-click your file in the lower part of the window, and Add Root Categories to Selected File(s)
Select /Default/Figures/People/ (include any deeper subcategories you want to add for filtering, like Male/Female, Fantasy/Scifi, etc. You can Add Root Categories multiple times if you want to add more than one filter)
Now your character will show up in Smart Content under Figures, for easy adding to scenes.
No need to right click>Merge with this method. Once you have the metadata set right, you can just drop characters into your scene at will.