It started working again now, by itself. Here's a complete summary for anyone else experiencing similar issues:
Situation: The home button didn't work. The fingerprint and double tap actions worked, but the click and double click did not.
Over 5 days I tried the following actions (For help with the bold actions, see the guide I linked to above):
- First I performed enable Assistive Touch to be able to use the phone at all. Note: It can be tricky doing this when the Home button doesn't work. You may have to muddle around with things like opening the camera first, unlock with fingerprint, switch the screen on/off, use favorite apps (swipe right) or use Siri, simply to get into the Settings app and enter the Accessibility menu.
- After that I explored various settings making sure I hadn't changed anything
- I confirmed the button was clean, not physically damaged. I also tried plugging in a power cable, to add some back pressure when clicking.
- I tried powering the phone off and restarting it several times including forced restart.
- I tried to recalibrate the home button. I did this 10 times in a row
- Then I tried reset to standard settings
- Finally I removed the back cover and enabled back tap (Settings > Accessibility > Touch > Back Tap), to make the phone somewhat useful, since this is easier than assistive touch. Note: The back tap was sluggish and didn't work very well to begin with.
By now the Home button still didn't work, however:
- Several hours after enabling back tap the home button started working again - very sluggishly. I really had to massage and "press" hard (It's not a physical button so "pressing hard" shouldn't do anything). In the mean time I had been using both back tap and assistive touch interchangeably.
- Gradually the button started working better and better, while I kept using it, and now, one day after, the button is back to normal.
I have no idea what is going on, but my best guess is that all the steps above got something reset, restarted or recalibrated.
I figure I may not be the only one with this problem. Therefore the comprehensive guide. Best of luck, if you have a similar problem. Use the guide I linked to, or google similar videos using keywords in bold. Video guides really helps a lot.