It’s definitely hardware. I had the same problem and was driving me nuts. Wouldn’t respond frequently and typing was impossible. It then started shutting down after a full charge and there was a slightly brighter spot in the middle of the screen . My suspicion was that the battery was done and had expanded. I’ve always had my iPad in a ridiculously protective case with glass screen protectors and all that. I had tried multiple restores etc. Anyway I got the battery replaced at apple store to fix the shutdown problem and restored from backup and it works as it should. Still disappointing and now I suppose likely to happen to this ‘new’ iPad .. Just in case it helps. I think it’s all related to battery which is why it develops over time.