hi Welcome to the forum.
Bit strange ,I would normally have suggested reprogramming the keys to the car but you have already done that, and some functions seem to be working.
I notice a 2012 jazz has 6 fuse slots labelled as door lock fuses, positions 27,35,36,38 ,49,50 . I am not sure how a flat battery could have caused fuses to somehow blow. But the quantity of fuses does suggest to me that it may not be as simple as one fuse and power feed serves for both locking and unlocking in each individual door.
5 fuses may make sense - one to each door and one to the boot, but 6?
But beyond that I cant help much. There may be a central control unit that divides the wiring , not individually to doors, but for instance, one control unlocks both left doors, another locks both left doors, another feed unlocks both right doors etc. In this way a single failure wouldnt completely disable one door, but would half disable 2 doors . If that makes sense. (a bit like lights are often fused separately for left side and right side, so if one side blows the other side should still be lit)
I dont know if there is such an arrangement or where it might be located. Try locating as many wiring loom loom connector blocks as you can (especially those near the car battery ) and give them a good joggle to see if there is a poor electrical connection,. The connectors may have been disturbed during the battery change, or indeed the source of any parasitic battery drain that flattened the battery.
