Just in case anyone else is looking for this info, I figured I’d share what I found…
The Trimble Connect Web viewer and Trimble Connect Desktop versions have significant differences in features.
The Web version does not give you access to your model hierarchy, however, the desktop version does. You can find, in the “Models” panel, basically what you’d find in the Outliner window in SketchUp. From here, you can hide objects (meaning, your SketchUp groups and components).
I’ve also found the SketchUp model layers, but it is very buggy, and only shows some of the layers, and not all objects are correctly represented by the layers that do appear. In other words, it’s a useless mess. But if you click the Objects panel, Group by: layer, you can see (some) of your layers.
Finally, SketchUp Scenes do not import into Trimble Connect, but they have a similar thing called Views. You should be able to configure visibility, camera position, (maybe other things??? It appears that selections are saved in a view too???), and save those to a view. But I’m having an issue where when I try to recall a View that I saved with mixed object visibility, the entire model becomes hidden. However, if I sync the model to the cloud, and recall the View in the web version, the View appears as expected.
Trimble Connect is still extremely unreliable and buggy, but hopefully it will continue to improve.