If you have tested the home button on your original cracked screen and the touch ID functions but does not “click” then the home button is damaged and replacing the screen probably wont fix it. The home button has a U10 IC on the home button flex that if replaced should fix this issue as long as there is no other damage to the home button. You will need to have the home button sent to a repair centre that can perform micro soldering and can replace that IC for you.
This is a common issue in the iPhone 6S. If I am not mistaken the Tristar IC is faulty/ damaged. It can be fixed/ replaced by a repair centre that can perform board level repairs. I work at a repair centre and get quite a few iPhone 6S devices in a month with this problem and I have it repaired at a board level repair centre and it fixes the problem. Check in your area for a repair centre that can perform board repairs and this should sort out your problem.
Hi Guys, I have picked up that if the screen you are trying to use is not truly an original screen then you will run into this pairing issue. I work at a repair centre in South Africa and I had a few of these Apple Watches come in with this issue after we had replaced the screen. Only when I tested the watch with a new ORIGINAL screen then they would pair it with an iPhone.