Several factors can cause milky white water. One of the most common reasons is the presence of air bubbles in the water, which can occur due to changes in water pressure or a disturbance in the water distribution pipes. Another possible cause could be the presence of sediment from nearby drilling activities.

It’s important to note that milky white water can signify bacterial growth or other contaminants.

If effervescence were to be the cause, then the water should have cleared after a few minutes. The most common cause is calcite precipitation. If you want to check for this, just add vinegar or any acid, stir and it should clear up. Pouring out water releases CO2 and if the water is supersaturated with respect to calcite, the calcite will precipitate as fine crystals suspended in water. If acid does not clear the color, then there may be abundant bacterial slime in the water.

Adding to Anthony Gorody's response, perhaps the water tank previously built up 'scale' mineral deposits on internal metal surfaces (especially if water stored was warm or warmed inside tank), some of this 'scale' may have recently broken loose and has been slowly breaking up into small particles and also perhaps slowly dissolving in the tank water, especially if water has been getting cooler. If you had a way of gently getting in a small immersible camera to photograph the interior surfaces of the tank (at short distances due to some presumably translucent milky water color), this might 'clear up' the mystery fairly quickly.

This may be due to presence of some gases in water, these gases dissolved in water with the formation of white solution,