Cannot restore backup or update because not enough storage space

I'm on a Windows 11 computer trying to update my iPad (not sure about the exact model, but I know that it only has wifi capability). Unfortunately, this iPad only has 32 GB of storage space and is full, so I try to update through iTunes so that the update file can be stored on my computer with plenty of space. iTunes tells me that I need to free up at least 900 MB of space before updating, so I try and delete some unnecessary apps, photos, etc. For some reason, the space usage doesn't update because I still can't update my iPad despite freeing up multiple GBs of space. I tried unplugging and restarting the iPad to no avail.

From previous experience, I know that storage space can often be freed when you restore from a backup, as the OS is refreshed. iCloud is full, so I make a backup on my computer and try to restore it. This time I am met with the message, "Cannot restore backup because there is not enough free space on this iPad." So, I delete literally everything from the device since I already have all the data saved. There are now over 20 GBs free on my device. When I try to restore the backup, I still get the same error.

At this point, I'm pretty sure there's some glitch, so I try to repair my iTunes application through the Windows settings app and check for updates (there are none). It still doesn't work, so I start doing some online research and found out that after a factory reset this problem can often be fixed. So I reset my iPad, but still can't restore the backup. I thought that it might have been a problem with this version of iOS, so I try once again to update my iPad. This time it does work. I am able to install iOS 15.3, but I still need to restore my previous data. I attempt one last time to restore the backup from my computer, only to once again be met with the "Cannot restore backup because not enough space" error even though I am now actually incapable of freeing up any more space. So now I have an iPad with the latest version of iOS installed stuck in factory state because I cannot restore the backup that I made.

It is worth noting that every time I get the "Not enough space" error, my iPad restarts itself, but otherwise, I have no further insight into this problem. I've also exhausted all troubleshooting steps I know of, so now I'm here.