Reduce wine in a 2-qt. saucepan over medium-high heat until 1 tbsp. remains. Pour wine reduction into a bowl and set aside; wipe out saucepan. Heat oil in saucepan over medium-high heat. Add onions and cook, stirring occasionally, until soft, about 10 minutes. Add beet cooking liquid and wine, along with the port, vinegar, and sugar; cook, covered and stirring occasionally, until onions are tender and deep red, about 20 minutes. Season with salt and let cool to room temperature.