Hmmm, this is a pretty weird error message to get from mbedtls. It makes me wonder if the exact webservice is using some esoteric algorithm or tls technique that mbedtls just doesn’t support.
If you update to HTTP.jl 1.5 (released today!), you could try switching to OpenSSL.jl as the TLS provider, like:
using HTTP, OpenSSL
r = HTTP.get(url; socket_type_tls=SSLStream, require_ssl_verification=false)