Not the OP, but I guess the power of Raspberry Pi is that everyone already has one - really useful if you want to do something in a hurry without anything extra. I've used a Pi as an emergency programmer on multiple occasions, as an SPI flash burner, as an SWD debugger, as an AVR programmer. You can even use the Pi as an USB-FDD bootdisk or emulate an IDE driver via its parallel interface.
Basically I don't want to have to be constantly moving a usb disk around.
Don't get me wrong: It would be possible to do it, but it would be theoretically not reliable, even if it felt reliable. You'd also need some sort of glue in between, as floppy drives signal at 5v and the rpi isn't 5v tolerant.
Therefore, you could connect the pi to the stm32, rather than directly run the floppy drive from the pi.
The problem with pi is non determinism, meaning you cant bitbang FM/MFM encoded data stream like the floppy drive. Smbakers project goes around this using dual port RAM implementing mechanism employed by for example 1995 DiskOnChip (m-systems, later Sandisk)