Well, it turned out to be the proximity sensor / ambient light / forward camera assembly.
On a side note, the iPhone 6s plus was given to me by my sister after she upgraded to an iPhone 12. The phone was alomst 6 years old and was out of warranty years ago. It had a badly shattered screen and the original battery that was bad. I later discovered the issue with the proximity sensor, and also discovered a non functioning accelerometer ic and gyroscope ic. She told me it had been dropped several times from table height as evidenced by the scratches on all four corners of the case and the phone was giving her problems for some time. I estimate the phone was worth less then $20 in the condition she gave it to me.
The only reason I opened it up was to see if I could repair it. I was able to get it working for under $40 (display screen, battery, and proximity sensor assembly). I was even able to tighten (and thread lock) the screws holding the taptic engine, which resolved the rattling noise when the phone was in vibrate mode. The only thing I did not repair was the accelerometer ic and gyroscope ic because I do not have the right equipment and I have no experienc soldiering circuit boards. The cost to have someone replace the ic chips would have cost far more then buying a certified refurbished iPhone 6s plus.
I inserted the sim card of another phone and it worked flawlessly, with the exception of applications requiring the gyroscope or accelerometer.
I agree with you all and had this been a newer model iPhone or under warranty, then the best course of action would be to get it repaired through authorized Apple repair facility. However, in my case, this iPhone would have ended up in the trash had my sister given it to me to tinker around with.
My 11 year old wants the iPhone I repaired. I am considering going with a $15 a month prepaid plan and giving it to him. I'll use it as a test to see if he is responsible enough to take care of a phone. If he shows me he is, then in a couple of years I'll buy him a brand new and better phone.