Traditionally the Chief Medical Officer has a positional authority over the Captain to stand down or remove them (or any other officer) from command on medical grounds if they believe it is necessary. This may hold true for wholly or partly biological based life forms which is their area of expertise but what about entirely technological ones like Data or the EMH if they officially held the Captain's chair?

Does the CMO have any Positional Authority over such individuals or does this responsibility transfer to the Chief Engineer for dealing with such wholly technological based entities in senior positions? If such an individual was suffering from some kind of damage that impaired their ability to perform their role would the Chief Engineer have the recognized authority to dismiss them instead of the CMO?

Bonus Question: Following the events of Picard Season 1, how might this question apply to Picard himself in the unlikely event he ever returned to active duty?