Alright, I found a fix for this.
You go into the settings shown on the picture above, select After Effects .exe and put the Power Saving mode on. It's not the best fix, but it doesn't seem to make the app completely rely on the integrated card, because so far I haven't seen any performance issues and the task manager shows the RX 560x to be using up resources, too. I've reported this issue to adm, so hopefully something will come out of it. Anyway, if you're some lucky fella who faces this issue that absolutely no one talks about like two years from now on - I dedicate this one to you. I put my blood and tears into finding a fix and now you won't have to go through the same things that I have. Peace.