Usually the GBuffer stores surface albedo, which is a 0-1 fractional/percentage value. A skydome is more like an emissive surface though, than a regular diffuse surface, so yeah, it doesn't make sense to render it into your GBuffer's albedo channels. When adding emissive surfaces to a deferred renderer, the usual approach is to render these surfaces directly into your light-accumulation buffer, instead of into the GBuffer.
I think the reason for the problem is a combination of drawing the sky to the gbuffer's color RT (which is a R8G8B8A8_UNORM_SRGB surface)
This is an interesting point to make, because most people would just render their skyboxes/skydomes in the albedo buffer and make it skip the lighting pass so it keeps its original color in the final render. So suppose if the sky is a blue gradient, you just leave the pixels black in the albedo buffer where the sky would be, and draw the shades of blue in the lighting pass? How would you apply sky lighting to all the objects in it? Usually, I lit everything in outdoor scenes with directional lighting.