The rapid growth led to infighting and management squabbles. And with Mr. Zuckerberg’s round-the-clock, hard-charging management style — his attention on a project is often compared to the “Eye of Sauron” internally, a reference to the “Lord of the Rings” villain — some engineers burned out and left. Executives hunkered down to brainstorm next steps, including potentially ratcheting back investment in Llama.

In May, Mr. Zuckerberg sidelined Mr. Al-Dahle and ramped up recruitment of top A.I. researchers to lead a superintelligence lab. Armed with his checkbook, Mr. Zuckerberg sent more emails and text messages to prospective candidates, asking them to meet at Meta’s headquarters in Menlo Park, Calif. Mr. Zuckerberg often takes recruitment meetings in an enclosed glass conference room, informally known as “the aquarium.”

The outreach included talking to Perplexity about an acquisition, two people familiar with the talks said. No deal has materialized. Mr. Zuckerberg also spoke with Ilya Sutskever, OpenAI’s former chief scientist and a renowned A.I. researcher, about potentially joining Meta, two people familiar with the approach said. Dr. Sutskever, who runs the start-up Safe Superintelligence, declined the overture. He did not respond to a request for comment.