the constituents and chemistry listing on the above pages should give you some of what you are looking for; note that there are several (thousands?) species of cordyceps though, some apparently having immunosuppressive effects.
You will often find the word parasitic associated with cordyceps because it is a parasitic\opportunistic fungus.
This is what is talked about when there can be, "good" parasites and "bad", like bacteria, and I would also guess virus as well. The "good", helping us, as a living organism, survive and adapt, the "bad", contributing towards our demise... a yin and yang. As an example, the "symptoms" of candadisis overgrowth is an environmental opportunistic response to conditions in the body.
Yeast: Friend and Foe?
Cordyceps Fungus
When one mentions or discusses cordyceps, it would be helpful to identify and define the species.
Here is a page discussing the cordyceps in maxgxl...
the first statement is a bit misleading using the word "rare" in the general sense and not as it applies to the specific species used. It also is a bit misleading, and misrepresenting by omitting the many various species, however, most likely does so to focus on the species\variety used in maxgxl.