What is the meaning behind the reference to yellow, black bile, phlegm, and their variations in strength in certain months in Tibb Al Rida, the book attributed to our 8th Imam Raza (as)?
This is a reference to the premodern medical theory of the four humours, which dates back to Aristotle. The idea behind this is that an imbalance in the four humours could lead to being unwell or different types of temperament.
As for variances between the seasons, I think this originates in a couple pre-existing models (which are not necessarily separate); that is to say, the text interacts with the ideas of the time and does not present something new. One is that, in traditional Chinese medicine, there are different recommendations for different times of the year. A somewhat less complex system is found in some countries (for instance, "hot" and "cold" foods), but I suspect it may simply be an idea that spread regionally and that is referenced here. The other is that, in the premodern era, medicine was often tied to astrology, and monthly recommendations can also be seen in this light.
May Allah always grant you good health!