I think it will be the Clinton/Obama neoliberal corporate clique who will make the first move since they have far more wealth and power and the real support from the corporate bigwigs. They can also do the most damage if they make the first major strike and end the internal struggle more quickly.
I think the first move in this scenario would be purging AOC and Ilhan Omar via a mix of both gerrymandering and airing all the dirty laundry they have to "cancel" them politically to make an example of them to the rest of the Woke Left.
The DNC will definitely go after AOC for her explicit enmity with Nancy Pelosi and pulling stunts like this, and this will likely happen even if Biden wins.
Omar would be purged from her office for her more overt anti-Zionist and antisemitic beliefs and because she's got a lot more skeletons in her closet that could destroy her politically such as her sham marriage, Islamist tendencies, and ties to Antifa and BLM.
The DNC is less likely to go and throw Ilhan Omar under the bus if Biden wins, though.