What would they be testing for with urine & blood in a toddler who is always thirsty & pees a crazy amount of clear pee?

Polyuria: Excessive thirst and urination can be a warning sign of diabetes. Blood and urine tests can be helpful in making sure this condition is not present, and can act as a baseline study for further investigation if warranted.

Sugar/electrolytes: Most 3 yo drink too much as a habit. If they drink too much they make dilute pee and need to drink. They could also have an inability to concentrate urine (diabetes incipidis) or diabetes (mellitis). Blood & urine can give a starting point for a workup.Habit drinkers have no sugar in their pee and get better as their oral intakes is weaned over time.