You are correct, technically Joe Biden was not a part of the government at the time that this email was sent. Do you honestly believe that this behavior is keeping with the spirit of the first amendment?
His team, and the DNC (here's one that's very similar, except that its from the DNC instead of the Biden team https://pbs.twimg.com/media/FjAuD6eWAAEFiXY.jpg)
are enormous and very powerful, and effectively a part of the government.
Do you think this kind of emailing Twitter and asking them to "handle" tweets they don't like, stopped on the day that Biden was inaugurated?