I think this idea comes straight from Biden, he's never been a particularly clever guy and people suffering from dementia/alzheimers often get paranoid and aggressive. I think he's probably harbored a hate for Obama because he's always been more popular, more competent, etc, and now it's coming out.

Also I don't really doubt Clooney and other DNC boosters/donors/officials would reach out to Obama, the guy who told Biden not to run in 2016 and 2020, to make sure they have his blessing. No orchestration really involved, just reaching out to the more popular, wiser, and not geriatric de facto "leader" of the party to make sure they're not fucking up by saying what everybody already knows.