Do the secretions that appeared after a wet dream—which are a transparent string with a reddish-brown tinge, followed by water-like secretions tending towards dark yellow—constitute istihadah (non-menstrual vaginal bleeding) that necessitates making up the days I fasted, or do they not affect ritual purity?

Cloudiness [kudrah] after four days of menstrual cessation is not considered menstruation. You should suffice with istinja (washing the private parts) and wudu (ablution) for prayer. However, if it is accompanied by the sight of blood, then it is considered menstruation, and ghusl (ritual bath) is obligatory upon you after the cessation of blood and any accompanying yellowness or cloudiness. The acts of worship you performed before seeing the blood are valid, and you are not required to make up the fasting of those days, because the purity (tuhur) that intervenes during menstruation is a valid purity.