Is it unhealthy to have too much anaesthesia?

Yes: It is unhealthy to have too much of anything. Anesthesia in particular. Fortunately, we have numerous ways to measure and 'titrate" the amount of anesthesia that is necessary, mostly by monitoring vital signs and the physical signs of anesthesia depth. Done carefully, anesthesia can be administered in the precisely correct amount.

Same as everything: The use of too much of anything is not really a good idea. In anesthesia we titrate the anesthetic you are receiving to what you need for the operation. The anesthesia machine allows us to monitor the drugs we give you, and decrease or increase them to fit your needs. If too much anesthesia is given the patient's blood pressure and other indicators will show this and we can correct the issue.