I have many scabbards like this. Since it's stitched in the middle it's probably wood inside, but if it's a modern production it may be plastic. If it's stiff leather with wood liners use super glue gel. Don't use leather glue. Just always be mindful and gentle when you're sheathing the sword and it should be fine. Plus easy to fix if it breaks again.
Personally I've had problems with leather scabbard repairs done with metal or brass shims because it causes a point of friction for the blade which can snag and scratch the blade, and many times it winds up breaking again. I received a previously repaired Napoleonic scabbard that is now useless because it has metal shims glued inside it and it has shrunken to the point that the blade won't fit, and now it has another break above the repair.