If we treat those multipliers of 6 and 40 as lower and upper bounds and apply it to the whole country, that's between 2.4 million and 16 million excess deaths. The best-run states have a smaller fraction of the population, so the real number is probably closer to the upper end.
So perhaps 5-10 million deaths in India is what we are looking at, with values both below and above being plausible. For comparison, the official death toll for the whole world is about 4 million right now.
(1) this is a crude extrapolation from ~5 states to the country,
(2) the underlying data quality is unclear to me; these journalists seem diligent but I haven't investigated their methods in detail and there is more variation from year to year than I'd expect,
(3) some of these estimates actually end before the worst of the recent covid wave, so they are likely underestimates, but
(4) there are some other biases that cut the other way. And
(5) not all of these deaths would have been directly because of covid, but indirect deaths - such as through loss of access to medical services - matter too.
EDIT: The numbers above imply that in the last 15 months, about 50-100% more have died each day as compared to the pre-covid period. The 'normal' pre-covid death rate seems to be ~26000 per day. If you use my very crude estimate of 5-10 million deaths and assume that the pandemic has been in India since April 2020, there has been an additional ~11000 - 22000 deaths per day since then, a ~43-86% increase.
Updating this list of articles about those -level excess mortality estimation (h/t to Rahul for the UP link):
https://scroll.in/.../madhya-pradesh-saw-nearly-three... (Madhya Pradesh, 42X)
https://www.article-14.com/post/untitled-60cf605395758 (Uttar Pradesh, 43X)
https://www.thenewsminute.com/.../karnataka-recorded-102... (Karnataka, 5X)
https://www.thehindu.com/.../excess.../article34870624.ece (Karnataka, 6X)
https://scroll.in/.../assam-saw-28000-more-deaths-than... (Assam, 30X)
https://scroll.in/.../andhra-pradesh-saw-400-increase-in... (Andhra Pradesh, 34X & Tamil Nadu, 7.5X)
https://www.thehindu.com/.../exces.../article34834150.ece... (Tamil Nadu, 4X)
https://indianexpress.com/.../coronavirus-jharkhand-door.../ (Jharkhand, 2X)
https://twitter.com/ChinmayTumbe/status/1407242935003803649 (Odhisha, 12-30X, not very clear)
https://www.thenewsminute.com/.../tnm-exclusive-kerala... (Kerala, 2X)
https://www.thehindu.com/.../chhat.../article35067172.ece... (Chhattisgarh, 4.8X)
https://www.thehindu.com/.../excess.../article35118826.ece (Rajasthan 5.4X, Andhra Pradesh 18X, Kerala ~1.3X, Madhya Pradesh 24X, Tamil Nadu ~5X, Karnataka ~4X)