On many of the newer generation iPads, it's actually normal for the display to wig out without the digitizer connected. I have experienced this myself in an iPad 7. I nicked part of the cabling for the digitizer, getting it out so I initially thought the digitizer was bad (it was) but was very confused when it did it without the digitizer connected at all. Come to find out iPads just do that.
More than likely your replacement digitizer is faulty.
I am curious about the home button issue, but I will have to read this in the morning when I'm not half asleep for that one. Poking though the answers forums here is FAR better for my mental health than doom scrolling Facebook before bed. But it sometimes means I'm sleepily answering things and brain no worky good.