Okay, I played some more. Stellaris is great, if you need a nap.
There's really not much to do. The occasional event fires, I was spreading some sort of gas beings across my empire, getting bonuses to social research on gas giants I couldn't otherwise use, and I collected animals for a zoo, but mostly it just made me sleepy. The one war I got into today, a fleet twice the size of the one I had took down a station, bombed a planets defences off, and then left. I slowly built up an equivalent fleet, took out one of it's stations, bombed a planet down, and never saw the enemy fleet.
It's the pacing close to CK2, years between wars, etc, but it's not an event driven experience, so basically you're just sitting there looking stupid unless you're at war, and even those aren't particularly interesting.
I'll probably read up on it in a year or two, see if it's gotten more interesting.