In the other manga he can't use the arm at all. It's basically just a decoration and he might as well have just lost it at that point, but I guess they wanted to tone down the violence or smth. But yeah, the oneshot here is pretty much a compressed version of the novel's prologue, the other manga focused only on a few key points from it and stretched them out to fill the chapters

When i first got into the one shot chapter here of the Crybaby Mage I already knew its way more closer to the source amterial than the series. Because I swear I read the novel and I KNEW MC LOST AN ARM. LIKE LEGIT LOST AN ARM. And they made it so that it was healed but not completely so he just can’t use it well???? Was so confused!!