I'll add here that that statement of Biden came as a surprise to some given earlier reporting...
Underscoring the single-term assumption was reporting like this from Ryan Lizza in Politico early in the campaign: “According to four people who regularly talk to Biden, all of whom asked for anonymity to discuss internal campaign matters, it is virtually inconceivable that he will run for reelection in 2024.”
I guess anonymous sources are worth what they are... Also, that was in Dec 2019.
On the other hand, his later statement was also commented upon as an "elastic formulation".
But after January 2021, some of his closest advisers indeed have indicated that he was considering it.
"He is planning to run again," Delaware Sen. Chris Coons told Politico over the weekend. "He knows that we are at the middle of an absolute turning point, a pivot point in American history. And he's up for the challenge." [...]
Coons is one of Biden's closest allies and advisers.
So, I guess it wasn't all that sudden of a change (if there was even a change), given that. Also, CNN notes that Biden himself gave a fairly similar answer in Aug 2020:
But by August, with Donald Trump ramping up attacks on the former vice president's age and ability to do the job of president, Biden was less vague about his future plans, Asked whether he could see himself running again in four years, he responded: "Absolutely."
The exact exchange then was:
“So you’re leaving open the possibility you’ll serve eight years if elected?” Muir asked him in a snippet of the interview released Sunday morning.
“Absolutely,” Biden replied.