Here is my recent travel experience:

Onward journey: \\
Travel date: 12/5/2021 - 12/6/2021 \\
Route: JFK -> New Delhi -> Vijayawada \\
Airlines: Air India (for all the flights including New Delhi to Vijayawada)
  * Air suvidha, rtpcr report, vaccination record - one hard copy was collected at the destination (Vijayawada).
  * In all other places (JFK, New Delhi), I just had to show the documents. They did not collect them.
  * I carried hard copeis. But had soft copies as a backup.
  * Print air suvidha in color (only on one side of the paper).
  * For the RTPCR test, it is 72 hours before departure (not arrival).
  * Luggage is only checked in till New Delhi.
  * I had to collect them and recheckin at New Delhi.
  * Customs, immigration, luggage transfer etc., took 3+ hours in New Delhi.

Return journey: \\
Travel date: 12/25/2021 - 12/26/2021 \\
Route: Vijayawada -> New Delhi -> JFK \\
Airlines: Air India (for all the flights including Vijayawada to New Delhi)
  * RTPCR test
    * should be done 24 hours before departure.
    * was checked at Vijayawada during checkin
    * was checked at New Delhi before entering immigration
  * Luggage booked all the way (Vijayawada to JFK). Did not have to collect or transfer it at New Delhi.
  * Immigration took a long time at New Delhi.
    * Long lines + very few employees.
    * I had 2 hr 30 minutes gap between the flights and it was not enough.
    * I almost missed the flight and had to run.
    * Suggest to have 3+ hours in between.
  * Immigration took long time at JFK also.
    * Long lines.
    * Flight landed at 6:30 am and by the time I came out it was 9 am.