I get the following error when I try to run my Qt application:
qt.network.ssl: QSslSocket::connectToHostEncrypted: TLS initialization failed
qt.net
Based on the information provided on the question, it looks like you have installed a too recent OpenSSL version. In fact I already had the same issue.
As you've found out, Qt does not embed OpenSSL. What you have to do is to install it by yourself. But you should ensure that you have the same (or the closest) version of OpenSSL than the one used for the Qt build.
qDebug() << QSslSocket::sslLibraryBuildVersionString();
qDebug() << QSslSocket::supportsSsl();
qDebug() << QSslSocket::sslLibraryVersionString();
Note: Don't forget to include the install directory to the PATH environment variable to make the dlls accessible (or copy the dlls).
Let me know if it does not solve your issue so that I can remove this answer to avoid unnecessary noise.