Actually, happiness does fact your Empire as a whole, and pretty quickly at that. I played a KOTH game where riotings were the key to the victory, as both of us tried to collapse our own economies by bringing the fight to the other side. I had half my planets rioting by the end of the game, and my opponent only had five planets not rioting, while many of these were not affected in any way by wars. (I had riots occuring in a system which was five systems away from the closest engagement)
I gather Stellar Manipulation does not affect happiness because there is no combat. The sun is blown up, and the planets are therefore destroyed by the wave following this event, but no battle ever took place. (Unless you were fighting a paranoiad ruler who put a few defences over the star, just in case.
)
If I understood how happiness is handled correctly, the actual consequences do not matter very much either, as killing a few billion settlers have the same effect as killing one million inhabitants. And it would be nastier on their morale to win ten battles against a single ship than destroying fourty ships in a single one. Add these battles turn after turn and you can find yourself faced with a full-fledged massive rioting in all systems of the Empire, save for your homeworld that is.