Just to add to the above, I erased all settings and restored the iPad to factory settings. Then I restored my backup from iCloud, re-installed the beta profile, and still receive the same error. I cannot determine whether the issue is device specific or on Apple’s end but given others are experiencing this on different devices, it is still difficult to determine the cause. My original thought was that it may be due to my iPad having a cellular connection but as this appears to be happening on some iPhones, it may not be the cause. Before I reset the device, it was asking me if I wanted to use cellular data if I get disconnected from Wi-Fi even though I did not have a cellular plan installed. I also was wondering if there is a partial download sitting somewhere but not showing up under iPad storage. i cannot reinstall the iOS 15 beta as that profile has been deleted and I cannot find it on Apple’s beta site anymore. Perhaps waiting for the next update of iOS 15 may resolve the issue.

One additional thought, perhaps the beta profile isn’t working with the particular hardware integration and therefore returns an error. Perhaps when the Beta 2 is out it may work.

Have not figured out a work around yet. I have done a clean restore to no avail. I have noticed on occasion that it gives me an error trying to download that I am not connected with Wi-Fi even though I am and it is working. When I reinitiate, I get the error in the image above.

Uninstalled the iPadOS 16 beta profile. Updated iPadOS 15.6 to the latest version which came out yesterday. Reinstalled the iPadOS 16 beta profile. Went to software update and updated my iPadOS to 16 and it worked. Typing this on my iPad with iPadOS 16 live.