You may want to crosspost this to /r/askfoodhistorians.

One thing to note is that your answer would vary hugely on the region and its preferences, and would also vary significantly on the food culture of that particular kingdom and personal preferences of the princes and kings. There is literally nothing called "Indian food" or "Indian princely food" as cultural and dietary differences are just too vast across India.

Another thing to note is that the good news is that this is actually one of the things that is extremely well documented. Many Indian kingdoms would maintain detailed documentation and ledgers on what the royal kitchens served, how many guests they catered, what ingredients were ordered and in what quantities. A good source for this is Raja Rasoi Aur Anya Kahaniyan which is a multi-part documentary available on Netflix and Amazon that researches the ledgers from the royal Indian kitchens across kingdoms and regions and talks about the food that was prepared in those kitchens. Every episode (season 1 has 11, season 2 has 24) covers one region of India and covers the notable royal kitchens from that region of India. The content is in Hindi but English subtitles are available so you can follow along. The name of the documentary translates to "King's kitchen and related stories".

To give you a few examples, if you were invited for lunch or dinner at a Rajasthani Rajput prince's palace, there is a very good chance that you will have wild game, for the Rajputs loved hunting. Typical fare would be partridge, fowl, wild hen, wild boar, deer. A typical dish that is served from wild game is Laal Maas. Laal Maas translates to "red meat" but the red here refers to the color imparted by a special type of deep red chili pepper. The dish looks fiery hot but actually tastes medium-spicy because the chili pepper is not super hot. Besides this, you will likely be served locally brewed wine and whiskey. The Rajasthani Rajputs took great pride in their palace brewed liquors (often flavored with exotic spices) and these were closely guarded secrets. Jagmohan whiskey for example is a fairly iconic palace whiskey - you can also buy it today as some of the princes have resorted to tourism and selling their palace whiskeys to make money. Very few people know about these Rajasthani heritage whiskeys even in India, although they are far more commonly known in Rajasthan.

If you ate in a Awadhi palace instead, be prepared for exquisitely and delicately flavored well balanced dishes. The nawabs of Awadh too immense pride in being true gourmands. The nawabs would play a very active role in telling the cooks what to cook and how to balance foods. They were also very adventurous and experimental. While Awadhi palace food was fairly rich and decadent, with a lot of emphasis on rich nuts like cashews, almonds, pistachios etc, the flavors were very delicate and used sparingly rather than being heavy handed. Flavorings and spices were often very exotic such as just a light touch of rose water or kewra and other essentials oils and aromatics extracted from flowers and herbs. There would be a lot of kababs (brought in from Central Asia through the Silk Route trade network), but again, focus was on delicate well balanced flavors and ultra soft texture. Galouti kabab is one such example. The story is that a nawab lost his teeth and still wanted to eat kababs so the chefs made a super tender kabab specifically for him. What sets this kabab apart from the rest is that the meat is ground very very fine, almost to a paste like consistency, spiced delicately, and then very gently shallow fried in a pan. Loud aggressive flavors were considered uncouth and uncultured by the Awadhi nawabs and even the people of Awadh in general. The very famous Indian biryani is also credited to be invented by the Awadhi nawabs. The story is that one of the nawabs was walking down the barracks and noticed a delicious aroma from the cooking pots in which soldiers were making their dinner. Turns out the soldiers would layer rice and meat and spices in a big pot and cook it. the nawab ordered his royal kitchen to adopt the dish and refine it and start serving it in the royal meals. And that's how the biryani became famous. The Awadhi nawabs took a lot of pride in their khatirdari (hospitality) and tehzeeb (sophisticatedness). The Awadhi and Delhi nawabs and princes were also heavily influenced by Mughal cuisine which in turn has its influences from Arabia and Persia. Urdu for example, which is the language spoken there, is heavily influenced by Persian and Arabic. Besides that, English influence also started creeping in, although arguably more in Delhi and less in Awadh, and even then, not as much as it influenced Calcutta and Madras/Tanjore.

Since your time frame is the 1930s, one thing to note is that the influence of the British Raj and British cooking sensibility was fairly well incorporated in the parts of India that were most exposed to the British Raj. That would be Bengal and Calcutta, and the South of India. Many of the royal kitchens in those parts of India adopted many British cooking sensibilities. In the Tanjore province in the South of India, Sunti and Kesari Maas were both quite popular, as well as a variety of seafood. Both are meatball dishes. Kesari Maas translates to "saffron meat". Being near the coast, there was a lot of use of freshly grated coconut and coconut milk, besides seafood and rice instead of wheat. And the province of Pudukottai and the royal palaces adopted British cooking quite a bit as well as British eating sensibilities such as usage of silverware, serving in British style serving pots, eating soup before a meal etc. A correction here: By this, I mean, Anglo-Indian cuisine which became a cuisine in its own right and is neither British nor Indian but both and with many new invented dishes. Such as Daak Bungalow Curry, Railway Mutton Curry, Devil Curry, Mulligatawny Soup (Anglicized from Milagu Tanni or pepper water), Kedgeree (Anglicized from khichdi - or rice and lentil cooked together and served with ghee - one of the most common and oldest dishes of India). Bridget White Kumar has written several books on the curiously delicious and less known Anglo-Indian cuisine. Her recipes are also available online for the interested.

For further reading on Indian food history, the definitive book to read is Indian Food, A Historic Companion by K.T. Achaya

Fun fact: Congee which is popular in the Southeast Asia derives its name from the Tamil word: kanji (also the Telugu and Kannada gañji, the Malayalam kanni and the Urdu ganji), from kanjī (“boilings”), referring to the water in which rice has been cooked.

I've barely scratched the surface. But I will definitely recommend Raja Rasoi Aur Anya Kahaniyan as a documentary that answers your question as it specifically addresses your question about what was served in royal Indian kitchens in the 1930s.