A loaded 'Barrel' can be loaded into the M3S to expand it's storage. However, a loaded 'Fire Barrel', despite having identical loading capacity cannot be loaded into the M3S unless it is closed and empty.
I am unsure if there is an intentional reason for this, if so then sorry for wasting your time!
Screenshots:
https://ibb.co/51W41CP - Able to drag barrel
https://ibb.co/2tWB0q7 - Unable to drag fire barrel
Place fire barrel close to back of M3S
Open fire barrel and load item into it, then close it.
Try click-dragging the loaded fire barrel into M3S 'barrel' expansion slot, but will be unable to do so.
If the fire barrel is empty and closed however, it can be dragged into the expansion slot.
Repeat above steps for regular 'Barrel' and you will be able to drag it into the expansion slot, even if it is open or closed.