iPad Air M2 overheating, lagging and eating through battery in Notes app.

I have the iPad (Air M2 11 inch 256GBs no cellular) for around two weeks now and use it mainly for notetaking for college. I've been having issues stated in the title, precisely: running iPad OS 18.0.1 and using the built-in Notes app with Apple Pencil Pro, nothing else running in the background, no internet or bluetooth connection (except the pen), low brightness (about quarter of the bar), both in light and dark mode, it happens (2 or 3 times so far) that the top right corner of the screen (with the camera in top center), where the CPU is I imagine, gets uncomfortably hot while handwriting gets laggy (today, I could write the next letter before the last one appeared on the screen) and the battery drains rapidly, at a speed of around 25% per hour.