Your integrated GPU of your APU has reached peak optimisation and been moved to legacy status, it will not receive any further driver updates. If this is a driver bug, it is not going to get resolved by a driver update. More information available here.
You did not mention which driver you are currently using, but the best bet would be to try the latest available drivers for your system detailed below, and see if either enables you to run the game using your dGPU.
You can download the latest Crimson 16.2.1 driver here.
You can download the last Catalyst 15.11.1 Beta driver here.
Thanks for your reply. I'm currently using Crimson 16t.2.1. I believe I've already tried Catalyst 15.11.1 but I'm not 100% sure of that.
I'll DDU the current one and try 15.11.1 (again) and post the result. Hopefully that will fix it.
Alright so I'm on Catalyst 15.11.1 now and set everything Overwatch and Battlenet related to high performance. Power play is on max settings and the general Windows power plan is on high performance as well. Despite all this, the game still selects the HD8650G instead of the HD8970M. After extensively looking at forums (which got quite boring) I'm starting to suspect that this issue is caused by the game itself rather than the AMD drivers. There have been many reports on the Blizzard forum of people having the same issue exclusively on a notebook with switchable graphics (AMD and NVdia). Not only that, other Blizzard games have been known to have this issue as well (WoW, HotS). I guess all I can do right now is hope that Blizzard is gonna fix this otherwise it's been 50 euros wasted. Thanks for the help Matt!