Has anyone had experience going from an old computer to a dedicated server?
Yes. Pretty much everyone involved in any decent level of commitment on this hobby has done that. Streaming from an "old computer" (as you say) general purpose noisy laptop or PC is not optimal for audio. It is not meant for audio.
Yep try to get Roon Core onto something like a Small Green computer to maximize the SQ. I moved off an old MAC mini and it was best thing I did for my digital setup.