I don't think that's remotely clear. No one in SPD's chain of command feels that way and they definitely don't take orders from outsiders.
> My guess is the mayor and/or the forces that pull her strings.
Certainly Durkan doesn't feel that SPD are a "malign force" — she's a former prosecutor and has only been supportive of SPD. Including and especially during the last few weeks. She also doesn't have the authority to direct SPD, aside from appointing a police chief. So she has some sway over Chief Best, but she and Best are buddy-buddy. And Best has consistently claimed she (Best) did not order the withdrawal.
My best guess is it was a political / tactical retreat by a lower-level leader to end the violence and save face. That or union action by East Precinct officers — they just didn't want to be there anymore.