Jasmine in High Desert: White Dots Not Fungus, Large Pots Cause Rot

The tiny hard white dots are not an "internal fungus"—online forums are unreliable. They're likely scale or natural root buds. Your large, oddly shaped pots (12–16 inch rims, 18 inches deep) with bark mulch keep soil too wet. Watering every other day is probably too much. Repotting isn't practical. Reduce watering, remove bark, and accept that flowering may be limited in your climate.