I need this cable

Yes the sensor cable needs to be connected and working. Apple in this series requires the sensor to be calibrated if you change it. Also note a new part will not have the sensors firmware downloaded to it yet so that will require access to Apple's paywall tool by buying the part directly from them (see the lower answer segment)

Getting a used part is the cheaper way and the magnets frame on the lids side can be rotated you should be able to dial in the adjustment by carefully rotating the magnet so the sensor already programmed setting is reused. With the newest macOS you can also review your parts and by pass Apples serialization as they caved on it. Sadly many used parts houses only have the new part presently which depending on your OS level maybe an issue. I haven't tried the onboard recalibration process yet on this series so I can't tell you if it works or not.

Here's the details on the needed part: Lid Angle Sensor 661-23648

To get the part directly from Apple from their Self Service site Apple self-service Repair just go to the #2 option to order it and the Apple official repair manual is here 16" MacBook Pro (2021) repair manual