Sleep mode includes “5.3.3 System OFF mode” and “5.3.4 System ON mode” as described in the datasheet. I am using “System ON mode”, which is not expected to save much current, but can easily wake up the internal RTC. 110uA seems to be the limit for “System ON mode”.
In my sketch, the MPU sleeps in “System ON mode”, the QSPI Flash sleeps in “Deep Power-Down mode”, and both wake up with the internal RTC interrupt and can write to the QSPI Flash normally.
I suspect (but have not confirmed) that the QSPI Flash wake-up method is the same in both “System ON mode” and “System OFF mode”. Please try it.