Is there any way to get a report on your own population like you can for rival factions in the diplomacy screen? I can't find any such report, and while I suppose I could hypothetically sum all my populations per planet, I'd like an easier way to check.

Not currently, but we could add something like that to the initial "vanity" screen (showing your own leader when you first enter diplomacy).

Not sure that would be all that useful, though. It would be nice somewhere down the road to have a more functional population summary screen.