the home button and motherboard as mated/matched/paired at the apple factory. only apple can re-do that programming when they replace the motherboard or home button or both during a repair.
the best that you can hope for is to get a 3rd party button (like a YF or JC) and a programmer (like a JC or a Quanli) and copy the ID from the original home button to the replacement button. unfortunately, if it works, the best you can hope for is the home button works and you will only get the Touch ID Unavailable when the phone starts from a reset/power-cycle. if you're not that lucky you will likely see IOS turning on Assistive Touch on-screen home button all the time (even when you turn it off) for IOS 15.6 and higher.