When it comes to military spunk, no Indian politician shows it off like Narendra Modi. The prime minister sometimes dons camouflage to celebrate Diwali, the Hindu festival of lights, with troops on the borders with China and Pakistan.

While inaugurating a film museum last month, Mr. Modi greeted the audience with a catch phrase from “Uri: The Surgical Strike,” a recent Bollywood hit about a 2016 military operation in which Indian soldiers entered Pakistani-controlled territory to take out purported terrorist training camps....