President Biden delivered the speech. He survived the speech. He had some jokes, got some laughs and provided some rousing economic commentary about the availability of Snickers bars and potato chips.

Then came the fun part.

“No one’s going to talk about cognitive impairment now!” Representative Jerrold Nadler, Democrat of New York, told the president after the speech, referring to all the concern about Mr. Biden’s age and his ability to handle the demands of the job.

“I kind of wish sometimes I was cognitively impaired,” replied Mr. Biden, perhaps talking about the speech he had just delivered. Or the stress of his job. Or House Republicans.

For at least 25 minutes after completing his State of the Union address on Thursday, Mr. Biden lingered with well-wishers who had gathered to praise a speech that had been energetic and more political than in previous years.

The president seemed happy he was done with his high-wire act, and for a while it looked like he would never leave. Speaker Mike Johnson and Vice President Kamala Harris chatted idly behind Mr. Biden as he circulated.

Finally, a House protocol officer told Mr. Biden that many in the chamber could not leave until he did.

“Are they Democrats or Republicans?” the president joked back, according to a reporter who saw the interaction.

Eventually, Mr. Johnson gaveled the session closed even with Mr. Biden still in the chamber.

The moment was a homecoming of sorts for Mr. Biden, who spent 36 years commuting to Capitol Hill as a Democratic senator from Delaware. He seemed eager for the praise. Before the speech, his allies had said he was craving interaction with people outside the gilded cage of the White House.

“As president, he doesn’t ever get the chance to just stop by and just engage with people,” Senator Chris Coons, Democrat of Delaware and an ally of Mr. Biden’s, said in an interview this week. The presidency, Mr. Coons said, had “made it harder than ever for him to just connect with people casually.”

Which is precisely what Mr. Biden did as the House chamber emptied and he stayed behind. He shook hands with some House members, including Representative Pramila Jayapal, Democrat of Washington and the chairwoman of the Congressional Progressive Caucus.

“I need you to bring that energy that you brought tonight,” Representative Nikema Williams, Democrat of Georgia, told him.

“I have too much energy,” the president replied. “That’s the problem.”

Finally, almost a half-hour after the speech ended, Mr. Biden departed a mostly empty chamber and headed home. He spent some time at the White House greeting supporters before finally going inside just before midnight.