I'm going out on a limb here and breaking with the consensus on this one.
When they wanted to drain the DS of the HWB 'ammo', they played up the testimonies and left HWB out of the conversation.
I don't think that Q and team would announce the RBG time of death or tease RBGs health state while also trying to bait them to use her for a delay or narrative shift in POTUS speech.
My thought is:
A.) Q team was responsible for RBG death and trolling the DS that she was executed.
B.) 2 tier plot where Q and team convince the DS that POTUS is hoping for another HWB reveal which would lead the DS into holding their cards close to the vest, allowing POTUS to deliver his speech uninterrupted as Q/POTUS actually want.