you camera is obviously not broken.
you have a betaflght setting issue or incorrect waring to your VTX
the way HD digital dose the OSD is the FC talks to the VTX and then the VTX draws the OSD your FC and VTX are not talking to each other
the common wiring mistake is the TX and RX wires are crossed, to should be TX -> RX and RX->TX. if your using the plugs you still need to double check it not every FC manufacture orders the pins the same way. DJI plugs have 6 wires if your are not using a DJI controller you can exclude the SBUS and the closest ground wire to the SBUS.
in betafligh you need to configure betafligt to use digital OSD its not setup that way buy default the easiest way is to use a preset JB talks about in this video
if you dont want to use a preset or its not available yet you need to use a few lines in the CLI instruction on what to type in are in the VTX manual sec 4.6 (page 18 and 19)