Don't tiptoe around the topic. By class you mean caste. As a white guy who has worked in tech for 25+ years and has made many Indian friends, I continue to be astounded by how fixated many (obviously not all) of them are on caste. In particular, how much time and effort gets spent trying to suss out each others' caste by asking questions like you noted. Every time we get a new Indian team member and the existing ones start asking him where his parents are from and I see him start to uncomfortably evade answering while all of the other non_Indians in the room have no idea what is happening, it starts to make ME feel uncomfortable.
Can't tiptoe around words I don't know :P I did say 'casual observer'! Thank you for sharing, reading to do. Seems related to my frustrations as a low-born but now well-made American.
edit: I say 'seems' here lightly; a system is conveniently reinforced by depriving participants words and the ability (or even desire) to identify. Time and time again the gut feeling is a well-established thing.
And as an Indian who has lived for 25+ years in India, I continue to be astounded by how fixated white guys like you are on caste when I have never once witnessed caste-based discrimination in my life, despite belonging to a categorized "originally backward" caste.
I hope that the caste system is on its way out though, although for that to really happen there need to be long-term societal reforms, just like with classism in e.g. Europe. Especially in the UK, working/middle/upper class is still very much a thing.