What is the ruling if the intention for purification is for a purpose not requiring it, without intending ritual purity?

Primary text

If one intends purification solely for a purpose that does not require ritual purity, such as cooling down, eating, trade, or marriage, and does not intend the prescribed ritual purity, the state of impurity is not removed. This is because the required intention was absent, resulting in no purification being achieved, similar to one who intended nothing.