The battery health is also included occasionally in the analytics the iPad sends to Apple if you have sending analytics. In Settings go to Privacy & Security/Analytics and Improvements/Analytics Data.

That takes you to a list of various recent analytics files that have been sent to Apple. If battery health was included it will be in one of the files "log-aggregated" files (iPadOS < 16) or "Analytics" files (iPadOS 16).

Battery health isn't always included in the analytics uploads so you might not have it in any of the files. Then you just have to keep checking as new files appear.

Here's a video I found talking about this [2]. The author of the video has written a shortcut [3] that shows up in the shar sheet. When viewing an analytics file you can share it with that shortcut and the shortcut will try to find battery information in that file and display it.

I just gave it a try but my logs don't currently have health information so I don't know how well it actually works for that. It did get cycle count from my logs and that matches what Coconut Battery shows.

[1] https://www.coconut-flavour.com/coconutbattery/

[2] https://www.youtube.com/watch?v=uQ_0l5pi7ro

[3] https://www.itecheverything.com/powerutil