Rules as written, there are no injuries like this. Literally nothing in the rules inflicts them, the rules don’t specify what effects they have on your stats or abilities, and so on.
Injury is entirely abstracted to the realm of HP damage, and to a lesser extent, ability score damage.
There are two references to the concept in the rules: regenerate, and the ring thereof. Regenerate can clearly fix a broken arm; it can re-grow an arm that has been entirely destroyed. (The ring can fix such injuries, but only if it was worn when the injury took place.) Presumably, re-attaching a severed arm is easier than recreating one from scratch, and certainly, healing a broken arm is much easier still seeing as that can be done in real life. This does suggest that there should be something less powerful than regenerate for healing such injuries, including a natural-healing option for broken arms.
But because the rules do not include these injuries as potential conditions for a character to suffer from, they also do not in any way address how they might be healed. The fact that regenerate references lost limbs is, itself, kind of out of place, since it effectively talks about healing injuries that the rules do not suggest can take place.
So from a rules-as-written perspective, these injuries don’t happen. Equally, from a rules-as-written perspective, how they are healed is effectively an invalid question: the rules cannot address a circumstance that the rules do not suggest can happen in the first place.
As such, any inclusion of significant injuries beyond these sorts of damage is entirely houserule, and when creating such a houserule the DM is responsible for detailing how these things happen, how they affect the patient, and how they can be healed. Ideally, these sorts of houserules are drawn up ahead of time and shared with the group, so that they know when they are at risk of such things, what the consequences are, and how to handle them when they do happen. (And you can also get into things like skill checks necessary to recognize such injuries, protect against them, help limit the damage done, help the healing process, and so on.)