What model is your Seagate?
From Arstechnica's review of the non-Touch 13":
"To that end, I plugged the Pro into the DisplayPort of a 4K Dell monitor I've got for this sort of testing. The 2015 Pro and Air could both drive 4K displays at 60Hz over a single cable, but they weren't great at it—even for basic desktop use, that's a lot of pixels for one integrated GPU to push. The new Pro still isn't perfect, but it's much better. I set both the Pro's internal display and the Dell display to their default scaling modes and opened up 10 windows on each screen, and then I used the macOS trackpad gestures to do things like switching between different full-screen apps and using Mission Control. The GPU definitely starts dropping frames when it's working this hard, but everything is more than fluid enough to be usable (this was also true with the 4K display set to 5K mode, something I wanted to test because the new Pros can drive 5K displays over a single Thunderbolt cable. Obviously, the higher the resolution and the more windows you have open the jerkier things get)."
I would think the Iris 550 in the Touch model would do a better job of course, but how much remains to be seen until we can get some good reviews.