Changelog for beta 3 is explicit that the upgrade will not work in many cases
Installer and Software Update
Known Issues You might be unable to update macOS Big Sur 11 Beta 3, if Secure Boot is set to No Security. (63434409) Your Mac might restart but isn’t updated to a newer version of macOS Big Sur 11 Beta. (65298753)
Workaround: Create a bootable installer using the createinstallmedia command. When updating to macOS Big Sur 11 Beta 3, you might be offered an unexpectedly large download rather than an incremental software update. (65753086)
Workaround: Under the “Another update is available” text, click the “More info…” link. This will reveal the incremental update where you can click the Install Now button. Personally, updating via the alternative 4.xGB upgrade, or the full 12GB installation, in both cases the system reboots back into beta 2.
I'll now look for the "Secure boot is set to no security", and try again, and if it doesn't work out, create the bootable USB media and try yet again.
PS: I've tried to upgrade my Mac mini first, which indeed has a T2, however I don't remember touching any setting on that secure boot utility on the recovery system. Still, it's good to know about those options, as it's important to be sure the setting to allow booting from an external drive is enabled, in case something bad happens to the internal storage.
Or maybe I just wait for beta 4…
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On Xcode, Devices and Simulators, your iPhone, if you click on the warning, then the details button, there's a long description stating your developer email and the exact URL that is not accessible.
In my case, if I login to developer.apple.com, and then try to access https://download.developer.apple.com/Developer_Tools/watchOS_18R5350e/Watch3_4_18R5350e.dmg it tells me I have no permissions.
So this is something to be fixed on the server side, not on the developer machine. Not gonna be solved by logging out and in or pairing devices.
I've double checked I've approved everything, and have my device UDID on the list, so not sure I can do anything else.
Bummer.
Update: I've noticed my developer certificate will expire tomorrow, so I've generated a new one, and now I can deploy on my watch again. Either the new certificate has reset something on the server side, or apple is already rejecting it even though there's still some hours left until the 11th of august. I'd recommend to double check your developer home page and see if there's anything to approve, if the device's are still on the list, and if your certificates are still valid and up-to-date. Hope this can help someone.