Had the same download error (check your internet connection (which is fine)) here when trying to upgrade to beta 6. But there is a pinned message from Apple in the DTK forum that you need to use the 'Beta Access Utility' to upgrade the DTK. After installing that one, the download works.

@DTS Engineer Having the same problem here: building an app on Xcode 16.0 on macOS Sonoma 14.7 results in an application that crashes on macOS Big Sur Intel machine with the same crash as mentioned above. Building with Xcode 15.4 does not have this issue. However, we cannot build this branch on Xcode 15.x anymore due to code changes for Xcode 16 compatibility. Is there a workaround? We're now stuck in an unreleasable state!

Good news for devs in this thread; Xcode 16.1 (last beta) fixed this issue (at least for my app).