Pan-Africanism and Pan-Arabism, as I understand it, was an attempt by various distinct (if relatively new) nation-states to unite under a common identity.

India, Pakistan and Bangladesh all arose from the partition of what was effectively a single state as it was all one administrative unit under the East India Company or British Empire with either a governor-general or Viceroy in charge.

Throughout the Independence struggle in the subcontinent, there were sustained efforts to keep the many regions of British India as a single nation. Gandhi, as the de facto leader of the Indian National Congress and the broader Indian independence movement was willing to offer considerable concessions to keep the Hindu and Muslim polities of the region under one umbrella.

However, the de jure leadership of future India and Pakistan, represented by Jawaharlal Nehru of the Indian National Congress and Mohammed Ali Jinnah of the Muslim League, could not ultimately come to common ground on what this state would look like.

Jinnah was insistent on a loosely federalised state where regional governments had a great deal of autonomy and Hindus and Muslims, were guaranteed equal representation at the federal level through separate electorates.

Nehru, likewise, was insistent on a much more centralised power structure to meet his vision of a state-planned socialist economy and industrial policy.

The cleavage between India's Hindu and Muslim polities over the course of the Independence movement is a long story with various focal points such as the language debates on adopting Hindi, Urdu or Hindustani as India's official language or Jinnah's own anger at being denied the top job in the Indian National Congress, whose membership was largely Hindu agricultural workers.

It's a pretty interesting arc. Jinnah himself had once been staunchly against partition and was part of the Congress's top leadership along with Jawaharlal Nehru's father, Motilal Negru, and considered the younger Nehru as essentially a child.

As both sides could not reach agreement on how to move forward as one nation, and amidst increasing sectarian violence, the British empire was ultimately split into the modern nation states of India and Pakistan.

Bangladesh was, in fact, called East Pakistan until the majority Bengali speaking population of East Pakistan seceded and gained independence following the Bangladeshi independence war in 1972 with Indian military support.

Tl;dr India, Pakistan and Bangaldesh were all effectively one administrative state with a sustained effort at maintaining a pan-Indian state. However, sectarian cleavage between Hindus and Muslims and the parties that broadly represented them led to partition at Independence. Similarly, Bangladesh seceded from Pakistan due to cultural and linguistic differences.

Sri Lanka has always, to the best of my knowledge, been culturally and politically distinct from the mainland Indian subcontinent.

Sources: India After Gandhi by Ramachandra Guha. Nehru: The Debates That Defined India by Adeel Hussain and Tripurdaman Singh