I had exactly the same issue a day after the official release of iPadOS 15 on my iPad Air 3. The only way to get out of this problem is downloading the 14.8 firmware and restore that image to the iPad. During all the years I've been using Apple devices this is the first time it failed so badly. Extra frustrations because of iTunes not working on Windows due to some problems with the latest release. But those are fixed. @Corlation you will have to restore your iPad. Reboot it, then get it into recovery mode, then restore 14.8 to the device. I hope you have a backup in iCloud, because this process will absolutely kill all the data on the iPad.