The problem is that you are setting the switch on a different AkComponent than the one in your animation.
With the Wwise integration, any object that makes sound has an AkComponent (much like the basic Unreal audio engine has AudioComponents). An AkComponent can be attached to any actor, or any component. In your case, two AkComponents are created:
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The first AkComponent is attached to the Player Pawn's root component. This AkComponent is created in your level blueprint, and it is used when you press 'F', and when you enter your Trigger Volume. This is why the switch "works" when you press 'F'.
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The second AkComponent is created in your animation, and it is attached to the Mesh being animated. If you're curious, you can take a look at the AkEvent AnimNotify Blueprint. In the Content Browser, go to Engine/EngineAnimNotifies, and open AnimNotify_AkEvent (make sure the "Show Engine Content" checkbox is checked in the view options). You can see that we attach the AkComponent to the mesh.
On the Wwise side of things, the AkComponent corresponds to a Wwise Game Object. What this means in your case is that you are not setting the switch on the correct Wwise Game Object, and this explains why your Set Switch node does not seem to work.
To fix this issue, you need to set the switch on the mesh. From the Level Blueprint, you can do something similar to this:
To help debug such issues, the Wwise profiler is very useful. In the Capture Log window, you would have seen that the "Set Switch" and the "Post Event" were being made on different game objects.
Hope this helps!