”William has the nebulous Royal Foundation thing”
The "Royal Foundation thing" cannot be nebulous due to the rules regarding the incorporation of charitable entities. The aims and objectives must be clearly defined. The Royal Foundation is focussed on conservation (including the Earthshot prize), early years, mental health, the emergency responders community and in the short term, on the response to COVID-19.
It raises a great deal of money: Of the £9.3m spent in 2019, £8.2m was spent on charitable activities, representing 87% of total expenditure....For 2018, this was £7.6m, representing 84% of total expenditure. More information, including the latest financial report is available HERE.
The Court Circular is the official record of past royal engagements. With regards to Prince William - while the length of each engagement is not shown, it's clear that a significant number of hours is spent on meetings with organisations that are supported by the Royal Foundation, in addition to meetings with patronages. Example:
17th March 2021
The Duke of Cambridge this morning spoke to Ms. Maria Wafer (Staff Nurse), Chest Clinic, Royal Victoria Infirmary, and Ms. Victoria Miller (Psychologist), Newcastle upon Tyne NHS Foundation Trust, via telephone.
His Royal Highness afterwards spoke to Dr. Liza Thomas-Emrus (Medical Lead), Ysbyty'r Seren, Cwm Taf Morgannwg University Health Board, Bennett Street, Bridgend, Mid Glamorgan, via telephone.
The Duke of Cambridge subsequently spoke to Dr. Alison Clarke (Assistant Director of Therapies and Health Sciences), Swansea Bay University Health Board, Port Talbot, West Glamorgan, via telephone.
His Royal Highness later spoke to Dr. Nicola Smallcombe (Respiratory Registrar), St. Bartholomew's Hospital, West Smithfield, London EC1, via telephone.
The Duke of Cambridge afterwards spoke to Dr. Kiren Collinson (Interim Deputy Medical Director for Primary Care), NHS England and NHS Improvement, Wellington House, Waterloo Road, London SE1, via telephone.
His Royal Highness subsequently spoke to Dr. David Arnold (Respiratory Specialist Registrar), North Bristol NHS Foundation Trust, Southmead Road, Bristol, via telephone.
The Duke of Cambridge later spoke to Dr. Thelma Craig (Consultant, Respiratory Care), Belfast Health and Social Care Trust, Shankill Road, Belfast, via video link.
There are days with fewer meetings, days with more meetings plus days with none. Only a fraction of engagements (meetings) are reported in the mainstream press, making it impossible to know for certain how many hours PW (or any royal) 'works' on average.