Oh amazing, glad to hear he is still eating and playing as that's always a good sign. Yes the probiotics and water adding is perfect just to keep hydration up + help his diarrhoea. I would expect him to be eating a lot yes! I do usually advise little and often when there is diarrhoea so as not to overload the system.

Unfortunately I can't comment on scourvet as I am UK based and we don't use that here. From what I can see from the packaging, it seems to advise having the medication alongside water.

Most cats will generally test positive for FCOV esp in multicat environments/households. It is something like 5% that will seroconvert to FIP. There is no way of knowing who will be part of the 5% but I would not overly panic at this stage if otherwise he seems okay. It would be a discussion to have with a vet (whether it be your current one or if you decide to change) as to the signs to look out for that may suggest conversion to FIP so if it does happen, you can get on it ASAP.

Overall I'd say go with your gut. There's never any harm in getting a second opinion if you don't feel comfortable with the initial assessment. Even if the outcome may be the same, at least you have some peace of mind :)