Any question answered...

Could someone please explain to me the shift to internal/integrated head sets?

If you wrap the headtube around the bearings you get a bigger head tube and more surface area on to weld interestingly shaped top and down tubes. I'm not going to claim Cannondale were the first to do this but they were at the forefront - it made sense for them. They called it the Si headtube. You get a bigger bearing, too. Stiffer + lighter at the expense of durability.

It happened more or less simultaneously with Bottom bracket bearings going outboards.

Not really - outboard bearings had been around a long time but Shimano and Campag hadn't really got on the train. Once Shimano did it became the accepted way of running a modern, durable stiff crank, but the tech had been around a long time. Pretty much at the same time - early 2000s - we had BB30 on top end race bikes.

I understand the BB thing as it let's you have a bigger axle in the same BB shell. But the headset thing is a mystery to me.

Outboard uses an existing standard and cludged a bigger, hollow, stiffer axle in to it. The advantages stopped there. BB30 and whatnot achieve this and more; the new, wider press fit BB designs let carbon bike designers do interesting things with chainstay length, clearance, downtubes... and linkages on MTBs. Outboard is a stop-gap.

Why would there be two almost opposite evolutions going on?

Outboards were an evolution and 30mm pressfit BBs + drop in headset bearings were a revolution. My race XC bike has headset bearings that are pressed in to the frame...with a headset press. Go figure :)