Obviously, the Akbar Birbal stories have transcended history, and kind of mythologised both figures far more than their actual historical achievements within a public consciousness. By some accounts, Birbal could certainly be considered a friend to Akbar, who supposedly lamented his death in Afghanistan, but it would be important to clear a few facts first:

Birbal was actually older than Akbar- something usually inversed in the folktales, particularly as presented in Amar Chitra Katha, haha.

Secondly, he was not that important: that is to mean that within the Mughal administration of Akbar's time, more importance rests with the Emperor, Abul Fazl and Raja Man Singh, and Raja Todar Mal: and most reputable history books, including popular history accounts of the Empire, note these figures far above Birbal. Birbal himself was perhaps more of a personal friend to the emperor than a distinctively important figure in the imperial administration: his rank was the same as certain Baghela, Bundela, and Rajput lords, but his compatriots would have had real political bases to draw power from: Birbal was more or less reliant on the Emperor.

In some ways, the Akbar Birbal myth can be seen as a distinctly 'Hindu' retrospective vision of the past that uplifted a Brahmin minister as a foil to the ruler, similar to Krishnadevaraya and Tenali Raman. And with arguably a greater focus on communal identities in modern South Asia, this emphasis on Birbal on Akbar's rule could be seen as a consequence of that.

Sources: Mannur, Anita; Rao, Sandhya; Sircar, Sanjay: The controversial Amar Chitra Katha comic books Bookbird (38:4) [2000] , p.32-36.

Justifying Defeat: A Rajput Perspective on the Age of Akbar, by Cynthia Talbot.