Having passed through Chinese immigration hundreds of times, I have a little experience with this. I am French, and currently visa free.
The attention the officer will give to your passport is generally inversely proportional to his or her seniority. The younger, the more thorough. An officer with only one bar and one dot on the shoulders will look at every page, even blank ones, possibly twice. An older officer will flip through it quickly, shrug, and start scanning the passport's ID page and Immigration for. It never fails.
Also, women always seem to be a little more strict than their male colleagues. When entering Mainland China, if there are a few lines for foreigners, you can predict quite accurately which line is going to be slower...
Now, regarding entrance into China. They are generally not concerned about how you made it in and out of the previous country. They might be concerned about countries you visited before China, but that's about it. They don't care about dual citizenship (as long as one of them isn't Chinese), since they don't recognize it. For the duration of your stay in the PRC you will be a citizen of country X, even if you have another citizenship.
China and India have an uneasy relationship, to say the least, so inspection of not only Indian citizens, but also Indian-looking people always takes a little longer. As far as I could witness, it generally remains polite, but you can feel the increased attention (and the queue slowing down). But the questions are about the intended trip to China, lodgings, invitation, etc, not the immediate past.
When leaving, airline staff will ask you about a visa for India, and will probably be satisfied with your OCI card, but again, Immigration won't care. Exit checks are very fast for foreigners (if there's no issue like overstay). They check your entry stamp, visa if applicable, stamp your passport next the entry stamp, and send you in your way.
UPDATE
Today (February 1, 2024), for the first time in hundreds of HK<>SZ border crossings, I was asked by an Immigration officer, on exit, where I was going. But even so, she didn't ask for a visa or my HKID. No idea whether it was something she does every time, or was curious (she leafed through my passport twice looking at every page, too, so I suppose she's of the very diligent kind).