Update and a whole lot of weekend drama. Hopefully this can be useful for others who have similar issues, although there's actually no concrete explanations.
Second round with the device, I managed to delete more apps so it has around 4GB of free space. It then finally could backup itself to iCloud. Ok, first objective done. Then the system data magically shrunk itself. I quickly initiated iPadOS update to 16.1.1 while the space is available. Long story short, the iPad finally got updated to 16.1.1. Thought we were done.
Then the system data enlarged itself again to its original state, taking up around 39GB of data. And it became a frustration for her as she would want to download some TV shows on Netflix for offline viewing. I finally suggested her to try resetting the whole iPad as we already have a backup. As a 2nd backup, we backup the iPad to her Macbook Air. The iPad backup itself is really small, less than 2GB. This shows that user data is not the issue.
Confident since we now had 2 backups, we tried resetting the iPad. And... it halted the reset process, claiming that her iMessage account is different from her iCloud account. Huh? There's only one iCloud account ever entered into the iPad. And the whole reset process froze. *sigh. Last resort, DFU mode. I told her we are going to reset the iPad anyway, so we would just do it with her Mac. Her mac runs the latest Monterey (she hasn't upgraded to Ventura yet). We connected it, Finder downloaded the latest iPadOS. So far so good. When it was time to prepare the iPad, the iPad glitched out. It kept boot looping to the DFU mode screen for a flash continuously. Finder on her Mac said unknown error. Yeah, very useful Apple. It kept doing that whenever we re-tried the whole process on her mac.
All seemed lost, but good thing I had my HP laptop. Yup, Windows to the rescue! I downloaded iTunes, connect the iPad, iTunes downloaded iPadOS, and... the restore was a success! Using Windows, and iTunes! Yeah Tim, where's your hardware-software integration?
But the drama has not ended. When the iPad rebooted and going to its first time setup screen, it showed that it was activation locked to her iCloud account. Sure, made sense. But it allowed us to just go through the setup process without entering any iCloud password! Wow, I though to myself, this is not a good thing. Despite that activation lock warning, we literally managed to just breeze through the first time setup process setting it as a new iPad!
Once we got to the home screen, we reset the iPad again by itself. No more activation lock warning. Then we restore the backup from her mac. It's working fine now, and system data is showing to be just less than 4GB. We just hope it won't happen again in the future, although based on a comment here, it might.
After all that, my takeaways:
1. iOS/iPadOS needs to have its own recovery mode. This is long overdue. We are supposedly in a post-PC era, and I still need Windows(!) to fix an Apple device. WTF Apple? When Windows and your old iTunes software can troubleshoot your own devices better than your own fancy new-ish OS, what does that tell you?
2. iPadOS16/iOS16 is a mess. My guess is there's something wrong with her iPadOS 16 OTA update process. Also, this made me afraid to do OTA updates. Do we have to go back updating our iDevices with iTunes/Finder for full OS update again to have reliable update? WTF with Apple's software team? Craig, stop being a salesman and do your effing job.
3. And what's up with that failed iCloud activation lock? That's not a good sign for security. This what led me to believe that iPadOS16 is the culprit.
Anyway, there's no guarantee this issue won't come back, and it seems that this is a long-standing issue on iOS for many years. The next time Tim Cook said anything about hardware and software integration, I'm going to laugh, remembering how we had to use Windows to fix the iPad.