Google search finds this:
https://thehill.com/opinion/white-house/4718993-did-biden-break-his-one-term-pledge/
That “transition” line is important, because it’s one Biden himself used publicly and on the record. “I view myself as a transition candidate,” Biden said at an online fundraiser in April 2020. In March of that year, at a rally where his eventual VP pick Kamala Harris was by his side, he used similar language: “I view myself as a bridge, not as anything else.”
As we now know, that turned into a bridge to nowhere. By March 2021, Biden was saying something entirely different. “My plan is to run for reelection. That’s my expectation,” he said shortly after he was inaugurated.
So Biden never explicitly made a one-term promise during the campaign, but he certainly implied it with the language of “transition.” You don’t typically think of eight years in office as a “transition.” And he had surrogates talking to their pals in the press planting the seeds of a single term, for a Democratic electorate that never saw Biden as their first choice, just as an acceptable consensus pick to take out the hated incumbent.