Very Sweet system, though I'm not exactly sure of the components related to Streaming. For example, if the Computer you are using dedicated to your Stereo System?
I would suggest you get a dedicated Streaming Device like Bluesound, Cambridge, or one of many others depending on your budget. That would integrate into your system very nicely, and could be controlled with a Smart Phone or Pad/Tablet.
That would also give you access to Hi-Res Streaming Services like - Dezeer, Qobuz, and the most popular TIDAL. Though it would also work well with Spotify.
Now based on your list of equipment, very nice equipment. However, that doesn't mean you necessarily like what you hear. If that is true, then we would need to explore specifically how the system was letting you down and focus on how to improve that specific aspect.
I agree with others that Room Treatments might help improve the sound. An open bare room can have a lot of echo that are not really noticeable because of the short delay times, but they will still cause the music to smear and blur.
While I'm sure HDMI will and does work, for music, as others have suggested, if this is audio only, I would consider USB. However, if it is Audio and Video then HDMI might be the better choice. Though be aware, you can probably have both.
I think you would benefit from the convenience of a dedicated Streaming Device. For example, the Bluesound NODE-2i is only about $500, and is very fast and responsive, and has a decent interface.
I think it depends on whether the Computer in question is dedicated to the System, or whether it is a general purpose personal computer.
Just a few thoughts.