The Court of Protection requires a medical certificate (COP3) to be completed by an expert with relevant medical experience and this forms the basis of most deputy applications. Usually the protected parties will have a GP or consultant doctor who can complete the application but there are other medical professionals who can also provide this service.
Assessing capacity is not something that a Deputy would do personally although an attorney must always be mindful of the protected party's cognitive ability at all times, as capacity can fluctuate over time and will vary from person to person.