Maybe this is OBVIOUS, but I lost 3 minutes figuring it out, so LFMP! (Learn From My Pain!):
There’s only one selectable object in this view, but when I Selected it, only a portion of it was highlighted:
This was baffling, until I switched to Edit mode: all the unhighlighted bits were Hidden. So a bit of a nice feature there, although if you needed something to remain Hidden in Object mode I’m not sure what your options are.
Anyway, hopefully this will save somebody 3 minutes of bafflement.