I guess that simply FAT is the default file system created in case of an erased flash.

However, when a firmware image is loaded then :

by default that board uses LFS2 as its filesystem.

Maybe, that means on a brand-new Blackpill when you load the firmware you will get a LFS2 filesystem. I have three more coming in a few weeks.

However, the original issue has not been verified by others.

The contents of the filesystem are removed, but the type of the filesystem appears to persist.

The type of filesystem is also an information that has been erased. As Robert said, it'll be encoded as a default in the firmware and therefore it looks and feels as it it's still there.

However, the original issue has not been verified by others.

I would like to try to replicate this, as I have a number of these boards with and without additional flash.

Is there a repeatable thing that you can document that triggers the "units stop working" bit?

The simplest unit that I have seen the application files disappear on is an IR transmitter, but it might be days/weeks/months before it fails.
Make a LFS2 filesystem and load:

import pyb

timer = pyb.Timer(2, freq=38000)
ch2 = timer.channel(2, pyb.Timer.PWM, pin=pyb.Pin('A1'), pulse_width_percent=50)

while True:
    print("Running")
    pyb.delay(2000)

Something I did not make clear at the start is that this happens on units that I put a LFS2 filesystem on. I will edit the first post.