In my humble opinion, I think the choice TZ made for India, by selecting Kolkata (formerly Calcutta) as the reference
location, was not a good choice.

Kolkata seems to have its own peculiar time zone history as the capital of West Bengal, staying on LMT or Bengal time until 1941 according to several sources.

TZ has chosen to use 'Railway time' between 1906 and 1941. This is not really the 'time used on the ground' by the population for all civil purposes, in Kolkata.

In addition, Kolkata is and was neither the seat of government nor the largest population center in India.

Delhi or Bombay / Mumbai would be better choices to represent India.

Both seem to have a cleaner time history and a much larger population than Kolkata: three times larger now, both 12 million compared to 4 million (the city, not the region).
In 1971, Bombay had 6 Million, Delhi 4 million, Calcutta 3 million.

Changing to Delhi, the seat of goverment, and second largest city, would allow for a more correct TZ zone representing all of India.

Regarding the detailed history of time in Kolkata, I have trouble finding newspaper archives.
I invite Indian readers of this mailing list to assist.

Of particular interest are the transitions in January 1906, October 1941 and October 1945.

References in the papers regarding clock time settings should be found.

The best reference for Indian time history I found in the book Horoscope Construction and Organisation by R.S.Chillar, who has an overview table.

Attention, the 4th column is shifted vertically, and two lines in the 4th column for West bengal appear swapped.

Sadly, his data make the history for Kolkata not clearer. Newspaper archives are really need to get the 'time used on the ground'.