Chosen Solution
This is a bit interesting. I’d suggest opening the phone first and having a look inside if you haven’t already. When you say you got the battery replaced, you mean by a repair shop? If that’s the case the technician working on your device may have not used the standard iPhone waterproofing seal, but instead just used glue or some other adhesive to bond the screen down, and that’s what may have caused the 3D Touch and home button issues. Open the device and take a look around the home button and frame of the device, and upload some pictures too. If the home button or screen were physically damaged in some way, they may need replacing, and unfortunately, replacing a home button means removing Touch ID entirely… Just have a look inside first and hopefully we’ll be able to identify the issue before replacement is necessary.
