How would you qualify the likes of Calicut or Cochin then?
Small coastal kingdoms comprising of multiple urban areas, with the capital city being the most important but not important enough to call the kingdom a city state.
(and its breakaway states)
It’s a little disingenuous to call them breakaway states- that’s like calling the history of France a regional history of a breakaway state of the Carolingian empire and ignores the difference in politics between the different states. While of course, the first generation of Indian sultanates drew on the abbasids for legitimacy, states founded by Indian converts and states founded after the sack of Baghdad in no way saw themselves as theoretical vassals of the caliph, and were no more inclined to jihad against the infidel than the mughal. In some cases, they were more secular than the Mughal state (cough cough raja Ganesh in the Bengal sultanate)
Even the Delhi sultanate rarely sought legitimacy from the caliph and mainly had their own names on coins. It was only when the current leadership was in crisis that the caliphs support was sought. Quite a few Delhi sultans established their own caliphates as well. This changed more with time and the revelation that abassid authority was non existent than due to the Mughals timurid genealogy.
None of the Deccan sultans of the Mughal era (who had none of the timurid genealogy to fall back on for legitimacy) gave any credence to the abbasids, and went so far in establishing their independence that they converted to Shiism.
On the other hand, Islam was an incredibly important source of legitimacy for the Mughal state, at least as important as their timurid legacy (though id say more) and it penetrated almost all parts of the state organisation. The entire reason they valued their timurid genealogy more than their chingisid ancestry was that Timur was suitably Islamic, and fit the dynasty’s self identification as ghazis. Of course they didn’t see themselves as vassals to the Abbasid caliphate, they saw themselves as the caliphate. Reference to Mongolic legitimacy was essentially a non-factor in mughal ideology, although it was referred to on occasion if the situation demanded it. In fact, when Muhammad Shaybani Khan conquered Samarkand, he claimed that he was restoring Genghis Khans yasa after centuries of timurid over dependence on the sharia.
All Mughal capitals were built in close proximity to Sufi shrines. In the list of 41 qualities that Chandar Bhan Brahman assigns to Shah Jahan- essentially a list of what gives him the right to rule only one makes reference to anything mongol (uses the term khaqan), one is a reference to Timur (second lord of the celestial conjunction, Timur was the first) three make outright references to non Sufi Islam (caliph, witness to splendour of Allah, the shadow of God), 18 make reference to Sufi terms and concepts (the perfect murshid, seeker of truth) and three make reference to his political power (protector of the world, king of kings, subduer of heavens). Of course, Sufi terms were far more common as many of these terms and concepts were in common with the Vedanta of the Hindus and thus assured legitimacy for both groups, but they are still fundamentally part of the Islamic tradition.
The akhlaq literary genre on how to live your life, whose main canons were all written outside India, were incredibly widespread under the Mughals and were suffused with Quranic injunctions and examples. While of course, the Mughals were more tolerant and more inclined to Sufi poetry that saw the equality of all religions (despite all formal religion being beneath true spirituality), this does not make them any less Muslim, it’s just that they took inspiration from different parts of the Islamic tradition. The qâżi and the ṣadr, like in all other Islamic states, had high politicoreligious positions; the Muslim divines, among others, had land or cash grants to pray for the stability of the empire and to maintain and keep aloft the symbols of Islam (sha’âyer-e eslâmi) throughout their territory. The periodic dispatch of rich donations for the holy cities, Mecca and Medina, with the delegates of hâjj continued. One of the chief accomplishments of the reign of Jahangir in his view was the full integration of the sharia into the law of the land. The Mughals definitely saw themselves as waging jihad to establish the supremacy of Sunni Islam, especially in the Deccan campaigns.
In short- if anything the Mongolian influence was superficial, and there was no Islamic gloss. The Mughal empire was self consciously founded and operated on Islamic principles, and went to great lengths to glorify Islam as they understood it and as it was understood by Indian Muslims.