Interfacing a STM32 MCU with an external ADC (and reading the data via SPI)
I'm no expert with STMs but for about every controller I've worked with, this wouldn't work for the following reasons:


Probably (I didn't check) you cannot access all 6 SPI interfaces simultaneously due to pin mapping constraints, even if you use only one MISO pin from each one; I'd guess it doesn't work out.
The six interfaces are all independent from each other, no way to sync the clock from Interface 0 to interface n. This is typically the case because the SPI peripheral is usually bought as IP, then instantiated 6 times; but there is no interconnection between those; they are separate instances with their own registers/memory regions.


What you should do instead is to read them as intended in serial (typically this is done through a DMA read). Since there is only one ADC inside and the maximum sampling rate according to the datasheet is 200k (8ch), assuming a 24 bit transfer (not sure if the STM's DMA can handle this) results in about 40 MBit data rate / spi speed. This should be possible, not accounting for post processing.