What do we know of the conditions the "prominents" were kept in in Nazi concentration camps?

As an example one could mention Kurt Schuschnigg, the Austrian chancellor who opposed the Anschluss. I quote here French Wikipedia, since the corresponding part is not present in the English version, but the story can be also found in Shirer's The Rise and the Fall of the Third Reich (alongside mentioning some other prominent prisoners):

Cet événement [Anschluss] lui vaut d'être incarcéré à la prison de Vienne, où il est logé comme un invité de marque. Ainsi, il s'installe avec sa nouvelle épouse, Vera Fugger (née comtesse Czernin), qu'il épouse en prison, en juin 1938. De cet amour naît en prison une fille, en 1941. La même année, lui et toute sa famille sont transférés, avec un traitement spécial, à la prison (Zellenbau) du camp de Sachsenhausen, où il partagea le même baraquement que Herschel Grynszpan, puis en 1944 à celui de Dachau. Le 4 mai 1945, aux derniers jours du Troisième Reich, un ordre d'exécution est lancé contre lui, mais il est sauvé in extremis par les Américains lors de la libération du camp.

This event led to his being incarcerated in Vienna prison, where he was housed as a distinguished guest. Thus, he moved in with his new wife, Vera Fugger (née Countess Czernin), whom he married in prison, in June 1938. From this love a daughter was born in prison, in 1941. The same year, he and all his family were transferred, with special treatment, to the prison (Zellenbau) of the Sachsenhausen camp, where he shared the same barracks with Herschel Grynszpan, then in 1944 to that of Dachau. On May 4, 1945, in the last days of the Third Reich, an execution order was issued against him, but he was saved at the last minute by the Americans during the liberation of the camp.

Hanna Arendt in Eichmann in Jerusalem discusses the Theresienstadt concentration camp used to show foreigners the supposedly human treatment of the inmates by Nazis, but also to hold the prominent prisoners, while they represented some value. Quoting again the Wikipedia:

Conditions in the ghetto varied depending on a prisoner's status. Most prisoners had to live in overcrowded collective dormitories with sixty to eighty people per room; men, women, and children lived separately. A few prisoners, especially those who had connections, managed to create private "cubbyholes" (Czech: kumbál) in the attics of the barracks. Some "prominent" prisoners and Danish Jews were granted private apartments in spring 1944 for the Red Cross visit. Even before the Red Cross visit, "prominent" individuals received better living conditions and more food, and their deportation could only be ordered by the SS (not the self-administration), resulting in a significantly higher possibility of surviving.

Also

Theresienstadt was known for its relatively rich cultural life, including concerts, lectures, and clandestine education for children. The fact that it was governed by a Jewish self-administration as well as the large number of "prominent" Jews imprisoned there facilitated the flourishing of cultural life. This spiritual legacy has attracted the attention of scholars and sparked interest in the ghetto.

The Nazis operated a wide variety of camps over the years, from extermination camps were victims directly murdered over concentration camps where victims were systematically worked to death to labor camps where survival was possible. Trying to average any number over all the different categories is difficult and likely meaningless.

On top of that, there were differences between the Sonderhäftlinge (special prisoners), and the status of any one prisoner could change over time. Some were singled out for torture, like the nobel laureate Carl von Ossietzky, others lived until liberation, like the pastor Martin Niemöller. It would be misguiding to average the daily rations of von Ossietzky and Niemöller, for instance.