For your remote working and K-Drama watching needs, just make sure wherever you're staying has decent internet. In a big city like Amritsar that shouldn't be difficult at all. Internet service in India is crazy cheap, so even a guesthouse that costs Rs. 1500 a night should have serviceable wifi.

For being away from "home", as a non-resident no one will sell you postpaid service so you're stuck with prepaid*. Jio or Airtel is the way to go. Jio will give you 25GB to use for a month for Rs. 300, or you can do the XGB/day plans for 200-500 depending on how much data per day you want. Airtel prices are similar. Buying a SIM card is painful, but Indian service is orders of magnitude cheaper than any of the roaming packages that work here if you're going to use a lot of data. If you can buy your SIM from the carrier shop at the airport, those guys are the least likely to be confused by the fact that foreigners exist.

*if you're visiting friends or family in Amritsar, just have them add another line to their postpaid family plan for you and cancel it when you leave. Offer to pay their entire bill for the month and you'll still be out less than 20 USD. Most postpaid plans come with amounts of data that are ridiculous by U.S. or European standards so you probably won't run them out. My wife and I share 520GB/mo. Not a typo.