First place to look is at the seatbelt buckle and pretensioner, possible the internal switch has failed so its not seeing the buckle inserted. You should find a replacement with one of our resident Breakers on here if you ask. Always disconnect the battery when disconnecting any of the wires under the seat to do with the safety and airbag system otherwise you will trigger an airbag light. Do not switch ignition on with any of the wires still disconnected to avoid an airbag light being triggered.
https://www.realoem.com/bmw/en/showparts?id=BT32-EUR-07-2003-E85-BMW-Z4_25i&diagId=72_0437