Well, the leadership did initiate a significant[1] national commemoration of QE2's death, even against a rumbling "What did the British Empire ever do for us?" attitude, reportedly. Hard to tell with India. Even 'simplified' with the post-Partition situation it's a complicated semi-superpower. One wonders what it would ever have been like if it had never been 'Empired' (British, Mogul, all the others back through antiquity) but remained more like the whole-lotta South-East-Asian territories vying upon various peninsulae and island-groups that have never been totally/permanently subsumed into Chinese, Japanese or all those many empire-striving European nations.
(But, of course, I must stress that "The Empire", did derive many benefits, including often overlooked contributions in WW1 (especially), from Indian manpower. Hard to tell how history would have progressed with no (technically) united India in our experience of the eras concerned.)
...umm, yeah, anyway, yes, I think India is indeed looking to be "the disinterested party", forging its own path. It has its own issues to worry about, in a nation with intense problems for much of its population but also a top-ten position in the world for a space-programme (Lunar landers, interplanetary probes, human spaceflight planned for the not-distant future (training its candidates in Russia!) and other things, though not without stumbling blocks) and famously an aspiring tech-hub which shows its breadth of aspirations on the world stage even if it finds its people (and environment) awkwardly unmanagable much of the time. I think that's a holdover from past "governance from afar", to be fair, which has not always been gloriously perfect.
But of course this means it's just a change of government (or nuance) away from being at the very least subtly more or less supportive of any other government, under their particular brand of democracy/etc.
[1] Yes, Biden also did the flags at half-mast on buildings/vessels thing. Never heard so much about Patriot/Tea-Party objections to that. And amongst their ranks they have those who object if Biden even blinks, who probably also strongly suspect that he actually doesn't ever need to.