China Daily reported that nucleic tests are not required from medium risk zones to travel. No mention of domestic quarantines for persons travelling from Beijing.
But basically it's business as usual: Right Hand, this is Left Hand.
There is no mention of medium risk areas in Beijing just high-risk ones some becoming a medium one. As far as I know, you need a nucleic test to leave Beijing if from a medium risk area though that now looks different if traveling by train no mention of bus, car, or plane whether elsewhere in China or overseas.