I used to be able to connect using a lightning-to-VGA/HDMI dongle, draw in an app like Goodnotes, and share+record that view. Sometime in 2018 or 19, they disabled this. The workflow I ended up figuring out involves connecting the iPad to a Mac via a lightning-to-usbc cable, starting a new movie (not screen recording!) through QuickTime, and selecting the iPad as a source. Then, you can share the view of the screen to an external display with acceptable latency and the ability to record the session. Be sure to select a mic, too, when you do this, otherwise the recording won’t have any audio. For some reason, it doesn’t start recording out of the default mic by default when selecting the iPad for the screen…
That’s a “iPad+adapter+OS” stack changed to “iPad+Mac+cable+QuickTime w/ tricky options” stack. If you’re one of the unfortunate souls owning a Mac w/o an HDMI port, throw an extra display adapter in there for Chaos’s sake.
It’s mind blowing how such a common workflow has become so obscured by arbitrary restrictions to OS functionality with no clear purpose.