The Hard Light blend mode on your glow is isolated to the "outer glow" layer FX. Once you flatten the layer and bake the glow style in, you lose the local blend mode of that glow in favor of the layer's blend mode - which defaults to 'Normal'
If you want that glow to real-time blend with the layers below it, you will need to leave it as an FX layer.
If you are satisfied with what you are placing the glow over, then you can merge your image.
Either way, if you need your glow to be set to Hard Light, then you need some content below it to 'blend' with.
Another option that might be better for you would be to:
- duplicate your layer & FX
- sample the colors you like from it
- set your glow to 'normal' and use that 'blended' color you sampled to approximate what you need.
You can get interesting results by combining a 'drop shadow' with no offset and an 'outer glow'. Set them both to 'Normal' and stagger their sizes to get a gradient effect.