When I was building the hospital, I managed to corner Zakalwe for a fairly in depth chat about the limits of medical science in Amber, and where Mandrake's role is in filling the gap between those limits and what we think of as modern medicine.
The basic rule of thumb is that medicine in Amber is roughly equal to medicine on Earth at about the end of the US Civil War. The basics are understood, but the details are still sort of fuzzy. The importance of sanitation is clear, but the germ theory of disease is just starting to be developed. As such, sanitizers in use are limited to simple chemicals, with alcohol (especially in the form of distilled spirits) and carbolic acid (phenol), which are excellent for sanitizing inanimate objects, but tend to damage living tissue when applied. Antibiotics are specifically nonfunctional in Amber.
Knowledge of advanced medical technology (beyond this level) is covered to an extent by the LIF-MP gift, which is a combination of supernatural healing ability and advanced knowledge of medicine in varying proportions from character to character. Extremely advanced medical technology, such as that available on modern-day Earth, requires the UL-Shadow lore to be familiar with, just like any other advanced technology.
LIF-MP, augmented by the other LIF-** gifts, allows a Mandrake healer to bridge the gap between Amber's technology and the results we expect from modern medicine. However, this does require the direct intervention and participation of the character, which is why the list of services in the hospital is broken down into things that do and do not require Mandrake attendance.