Why is the limit for rendering only 4096 pixels? It's 2024 and there is a lot of cases where you need more pixels, especially for multi projector installations etc.
The AE Export feature supports higher resolutions but they are dependent on the render resolution, which totally does not make sense.
For example when you want to export a 8000x4000 composition to AE, there is no way to set 8000x4000 in the render video settings. But the problem is that the aspect ratio of the render video settings are used to scale the AE objects, which also does not make sense as you wouldn't even use render video when exporting to AE.
The workaround ist to set a resolution in the render video settings that is within the 4096 limit and still the same aspect as the AE export settings. In this case where we have 8000x4000 px, you would need to set render video to 4096x2048 which is also 2:1. If you don't do that, your elements are squashed or stretched in AE.