This button do not have fingerprint recognition function, the touch ID are mached to logic board,  It is similar like iPhones.

That's means you can use the power on and off function only rather than the touch ID.

New Touch ID Power ON/OFF Button 821-04012-02 For MacBook Air Retina 15" M2 A2941 2023

Descriptions:

Product Name: Touch ID Power ON/OFF Button
Model:  For MacBook Air Retina 15" M2 A2941 2023

Compatible Model:                                                                                                                            

A2941
Mid 2023 For Macbook Air 14.15 15-inch A2941 EMC8301 MQKR3LL/A 8-Core M2 256GB
Mid 2023 For Macbook Air 14.15 15-inch A2941 EMC8301 MQKU3LL/A 8-Core M2 256GB
Mid 2023 For Macbook Air 14.15 15-inch A2941 EMC8301 MQKP3LL/A 8-Core M2 256GB
Mid 2023 For Macbook Air 14.15 15-inch A2941 EMC8301 MQKW3LL/A 8-Core M2 256GB
Mid 2023 For Macbook Air 14.15 15-inch A2941 EMC8301 MQKT3LL/A 8-Core M2 512GB
Mid 2023 For Macbook Air 14.15 15-inch A2941 EMC8301 MQKV3LL/A 8-Core M2 512GB
Mid 2023 For Macbook Air 14.15 15-inch A2941 EMC8301 MQKQ3LL/A 8-Core M2 512GB
Mid 2023 For Macbook Air 14.15 15-inch A2941 EMC8301 MQKX3LL/A 8-Core M2 512GB

Packing Includes:
1 PCS Power ON/OFF Button