This is likely exactly what has been communicated by the palace. Nothing more, nothing less. A precautionary admission to keep him under observation. Likely to make sure the medication is doing what it should and to prevent an infection from going to the heart, lungs or kidneys, wich in his age can quickly become critical...
The closest hospital to Sandringham is Queen Elizabeth’s Hospital in Kings Lynn (named after The Queen Mother). The closest University hospital with advanced specialist care should be Cambridge or Norwich to where i assume Philip would have been taken by ambulance, had his life been in danger. As that’s apparently not the case, his principal doctor decided to have him in where he/she works in London to keep him under observation himself/herself...
The Queen having been treated at the same hospital herself many times and knows its good quality, likely don’t want to put any extra burden at the hospital by being there herself and likely keeps contact with Philip over the phone. If things becomes critical, i have no doubt that she, Charles, Anne, Andrew and Edward would travel immediately to their husband and fathers bedside but we are not there yet and hopefully won’t be for a long time yet...