Touch ID works but home button doesn’t work.

Ouch, you've gone through a lot of screens!

I'm not sure if this is your problem or not, but I ran into a similar problem on my granddaughter's iPod Touch where the Touch ID was fine but the button didn't work after a screen replacement. I finally pinned it down to the little rubber nub on the bottom of the button that flexes the metal dome and makes the button click. Somewhere along the line I had apparently managed to knock that little nub off, meaning it took an inordinate amount of pressure on the button before it would click. I didn't find a guide for your iPad, but here's a picture of what you're looking for from an iPad 7.

That little black dot in the middle of the button is what you'll want to check. If it's missing you'll need to kludge up a replacement; for mine I found a piece of rubber, cut it to the approximate size and secured it with a dab of glue. The shape isn't critical; the original on mine was square so I just cut a tiny square out at about the same thickness. Don't worry about making it round; it's the height that matters, not the shape.

With any luck that's all that's wrong with your button; after three screen replacements I'd think it's very possible your little nub got knocked off, so this seems like a fair bet; at the very least it's worth checking.

Good luck; let us know what you find!