If waif wastewater-containing phosphates from laundry detergents made its way into waterways, such as streams and rivers how would that affect the water cycle?

Phosphate is a plant nutrient. In many surface waters such as lakes and rivers, algal growth is limited by phosphate, i.e., the algae have everything they need to have a population explosion except for phosphate. So when phosphate enters the water, the algal population then increases exponentially (an algal bloom). An algal bloom fundamentally changes the trophic state of an aquatic ecosystem. As soon as the phosphate runs out, the vast mass of palgae die, causing anoxic conditions as the plant matter rots. This often leads to the death of other aquatic organisms. Some algae also produce toxins.