Traditionally OpenSSH used the same private key format is identical to the older PEM format used by OpenSSL. (Because it uses OpenSSL for parsing the key, it will accept the newer PKCS#8 format as well.)
So the issue can be one of:
Your OpenSSL version refuses to load this key format. Perhaps it has accidentally enabled FIPS mode and refuses any algorithms except those part of its original FIPS validation?
Try loading the key into the
openssl command-line tool (which, yes, might also be linked to a different libcrypto, and you should check with ldd):
openssl rsa -noout -text < id_rsa
openssl pkey -noout -text < id_rsa
Try converting it to PKCS#8 format:
openssl pkey < id_rsa > id_rsa.pkcs8
Your OpenSSH has been built without OpenSSL support. Even though
ssh -V says the support was enabled, that does not automatically mean the
ssh-add binary is the same – it might come from a different partial installation.
type -a ssh and
type -a ssh-add to compare installation locations.
Once you know the path, use
ldd /usr/bin/ssh-add to verify that it's linked to
libcrypto.so (the OpenSSL cryptographic library).
If nothing works at all, try converting your key to the new OpenSSH-proprietary format using... PuTTY. Install the
putty package for Fedora, and use:
puttygen id_rsa -o id_rsa.newformat -O private-openssh-new
Also peculiar: GNOME somehow manages to add the key on login with seahorse.
Older GNOME Keyring versions have an internal copy of the SSH agent code and are independent from the system OpenSSH. So they will accept keys that your OpenSSH won't. (But on the other hand, this means severe lagging in terms of feature support (such as Ed25519 keys), and the latest GNOME Keyring just uses the system ssh-agent instead.)