The little yellow ones are
Leucocoprinus birnbaumii, a very common species in indoor flower pots. They've grown in some of my San Pedro pots on occasion. I'm not sure about the grey ones but in all likelihood they're growing on the compost and nothing to worry about.
San Pedros are very tolerant of moisture and, indeed, will grow like the clappers when given plenty of water and sunlight, especially when fed every 4 weeks with half-strength tomato feed. Thus, drying them out here is not strictly necessary - it would be interesting to find out what the grey mushrooms are - I once had
Panaeolus cinctulus (syn.
P. subbalteatus) sprout out of one of my flower pots...
Root rot is as likely to be bacterial as anything (that's what keeps getting my
Stetsonia coryne specimens - cold plus damp really isn't their thing). Fortunately, San Pedro seems to tolerate wetter soil and lower temperatures than most other cacti.
So, it seems you have nothing to worry about, rather you can be generous with the watering and find out just how fast your cactus is capable of growing!
“There is a way of manipulating matter and energy so as to produce what modern scientists call 'a field of force'. The field acts on the observer and puts him in a privileged position vis-à-vis the universe. From this position he has access to the realities which are ordinarily hidden from us by time and space, matter and energy. This is what we call the Great Work."
― Jacques Bergier, quoting Fulcanelli