I’ve solved the issue on my install. It’s probably not the cleanest solution, but it works for now.
For those who don’t want to wait, you can do the following:
# Install the dependencies for compiling curl:
sudo swupd bundle-add devpkg-openssl
# Clone the curl git repo:
git clone https://github.com/curl/curl.git
# The usual cd curl:
cd curl
# CMake, do your magic (make the Makefile and such):
cmake .
# Let's compile:
make
# ***Just some precautions to avoid nuking your install:***
mkdir -p $HOME/oldlib
sudo cp /usr/lib64/libcurl.so.* $HOME/oldlib/
# Last step but the one we need:
sudo cp lib/libcurl.so.* /usr/lib64/
With this, it works like a charm on my installation.
Edit: Fixed a few details.