It seems that the bug happens when registry name contains uppercase characters. I've edited my ~/.swiftpm/configuration/registries.json to lowercase the characters and then lowercase in the project SPM settings and it worked (discovered by my coworker somewhere on the Internet).

Filed as FB24035409. The post description said that Xcode 26 and macOS 26 work well but macOS 27 and Xcode beta (so Xcode 27 beta) don't work. So the problem is only on the 27 train (macOS and Xcode), both beta 4 currently.