In exercising discretion over how unverified or false content is moderated, social media companies have decided to “pick a side,” said Alex Stamos, the director of the Stanford Internet Observatory and a former head of security at Facebook.

“I think this demonstrates the limits of ‘fact-checking’ in a fast-moving battle with real lives at stake,” Mr. Stamos said. He added that technology platforms never created rules against misinformation overall, instead targeting specific behaviors, actors and content.

That leaves the truth behind some wartime narratives, like an apparent assassination plot against Mr. Zelensky or simply the number of troops killed in battle, fairly elusive, even as official accounts and news media share the information.

Those narratives have continued as the war marches on, revealing the contours of an information war aimed not just at Western audiences but also at Russian citizens. At the United Nations on Monday, the Ukrainian ambassador, Sergiy Kyslytsya, shared a series of text messages that he said had been retrieved from the phone of a dead Russian soldier.

“Mama, I’m in Ukraine. There is a real war raging here. I’m afraid,” the Russian soldier apparently wrote, according to Mr. Kyslytsya’s account, which he read in Russian. The tale seemed to evoke a narrative advanced by officials and shared extensively on social media that Russian soldiers are poorly trained and too young, and don’t want to be fighting their Ukrainian neighbors. “We are bombing all of the cities together, even targeting civilians.”

The story, whether true or not, appears tailor-made for Russian civilians — particularly parents fretting over the fate of their enlisted children, experts said.

“This is an age-old tactic that the Ukrainians are trying to use, and that is to draw the attention of the mothers and the families in Russia away from the more grandiose aims for war onto, instead, the human costs of war,” said Ian Garner, a historian focusing on Russia who has followed Russian-language propaganda during the conflict. “We know that this is really effective.”