Curious what level of brightness you usually use your new M4 iPad Pro on, as my iPad Pro has battery drainage issues (related to your plugging in and nothing happens) topic.
I've noticed with MY 2018 iPad Pro (A12X-based) 600 nits max brightness for me and 1600 max brightness for you, that the screen and battery can be strained if it's both: at a high-enough brightness level for long enough PLUS has been in any amount of heat for too long. One and not the other is bad enough for the iPad and both is even worse.
Hopefully someone at your local Apple Store can be of service, especially with this being the just-released newest Apple Product and all: (they'd be interested in double-making-sure to get it fixed for you.
Very much hoping your problem with your iPad Pro can be fixed. I can't imagine spending a day or a week without my iPad Pro, so as a fellow iPad Pro user, I feel your pain. I hope this helps!