Okay, so perhaps downloading is just a red herring and the actual problem is unpacking the content? Can you try this:
using Pkg, Downloads
# 1. Download file. Does this work and give you a gzipped tarball?
# The sha256 sum of this file should be:
# 95e32e3b3f797373f5f618786e6fa535949dd5b53d0d6cd72eae098a4342ac02
# for reference.
file = Downloads.download("https://pkg.julialang.org/registry/23338594-aafe-5451-b93e-139f81909106/60e2264e4b83c8920007abb1bc2440e990d108aa")
# 2. Unpack the tarball. Does this work and give you the expected registry
# tree in the tmp path returned?
Pkg.PlatformEngines.unpack(file, mktempdir())
Can you also try using the 1.7 beta (Julia v1.7.0-beta2 is now available - #3 by giordano) or the nightly build (Julia Downloads (nightly binaries)). From Julia 1.7 Pkg does not unpack the registry (but does for packages still).