Why India would go expansionist?
Expansion and Politics: India mostly wanted oil at first, and that was the justification for the invasion of Persia and the Middle East. After that initial wave, overpopulation was the major player in Indian expansion. All that legroom just ripe for the taking.... The fall of Rome was halfway underway already from civil wars and rebellions before India invaded Anatolia and North Africa to gain some more oil and finish off the coherent Roman State. The light purple states are not Indian state, per se, only puppet republics/kingdoms. They give large tributes in raw wealth to India in return for not being invaded.
These Roman territories are basically all mini-Romes with imperial systems of their own except for Brittania (commonly known as Britanistan), which is a loosely organized tribal kingdom, and the small Italian states, which are (mostly) republics. The Germanic and East European states are central or tribal monarchies with strong Indian and imperial influence. India itself is nominally a democratic republic; recently, there was a military coup after the expanded military funds were cut that placed a puppet President in charge who is re-"elected" each cycle. Africa is next on the list for expansion. India is barely staying together, but a very strong common religious identity and mission is enough for now. In fact, the new dark blue state in the East Indies and the independent Egyptian nation are both breakaway colonial nations that were let go of because of constant rebellions and issues in their area.
Technology: Things like germ theory, the idea of atoms, and some metallurgic improvements, as well as basic improved agricultural techniques like crop cycling and other things spread quickly to Rome and China, as well as cotton, bananas, corn, and soybeans, among other crops. Combustion and other such militaristic innovations are slowly making their way to China, as you can see by their partial conquest and puppetization of backwards Japan, while basic gunpowder and improved horse riding tools are catching on more quickly in the Roman territories. Innovation has practically ceased in India.
Religion: The Hindu ideas are getting pretty... interesting. The sudden shift into this new world has led to several more radical sects, and a new religious conservatism in India itself. The current new party, the
Bhaarateey Mahaanata Party (Indian Greatness Party) established by the coup is mildly theocratic, and the caste system is tightening once again. Christianity and Islam are targeted by radical Hindi groups in street warfare, and the new party does little to stop it despite giving lip service to religious freedom. Most of the world's Christians have fled to the Roman states or Judea, and it has found mild success in North Africa, Italy, and Gaul, as well as a large following in Judea bolstered by the Christians already there (who are very confused by some of the "new" Christians' doctrine and origin.) Several new Hindi groups with an emphasis on spreading the faith to other nations have created a new branch of Hinduism, Mahayana Hinduism. It is influenced heavily by Zoroastrianism and a small part by Buddhism, and it denies the validity of the caste system as its main deviation from mainstream Hinduism. They have managed to make it the majority religion in Southeast Asia, Egypt, Anatolia, the Middle East, and Greece. (Orthodox, mainstream Hinduism is still the far stronger faith due to the vastly larger Indian population compared to the rest of the world.) Mainstream Hinduism Zoroastrianism remains strong in Persia, though it is now in direct competition with Hinduism, both of the Orthodox and Mahayana types, and the educated elite have converted for the most part. Buddhism has spread to rural China, but no further, and many of its followers are looking to the far stronger Orthodox or even Mahayana Hinduism and wondering if it is the better choice. China has tried to suppress Hinduism, but the Mahayana variety is gaining traction among the peasants. Confucianism remains the Chinese philosophy and religion. New religions haven't spread to Japan in large quantities yet.