Can't push to github with SourceTree despite having identity added in agent: Permission denied (publickey) - github

Question

If I run ssh-add -l I see my identity in the list as expected. If I run ssh -vT git#github.com I get this output:
OpenSSH_7.9p1, LibreSSL 2.7.3
debug1: Reading configuration data /Users/myself/.ssh/config
debug1: Reading configuration data /etc/ssh/ssh_config
debug1: /etc/ssh/ssh_config line 48: Applying options for *
debug1: Connecting to github.com [140.82.113.4] port 22.
debug1: Connection established.
debug1: identity file /Users/myself/.ssh/id_rsa type -1
debug1: identity file /Users/myself/.ssh/id_rsa-cert type -1
debug1: identity file /Users/myself/.ssh/id_dsa type -1
debug1: identity file /Users/myself/.ssh/id_dsa-cert type -1
debug1: identity file /Users/myself/.ssh/id_ecdsa type -1
debug1: identity file /Users/myself/.ssh/id_ecdsa-cert type -1
debug1: identity file /Users/myself/.ssh/id_ed25519 type -1
debug1: identity file /Users/myself/.ssh/id_ed25519-cert type -1
debug1: identity file /Users/myself/.ssh/id_xmss type -1
debug1: identity file /Users/myself/.ssh/id_xmss-cert type -1
debug1: Local version string SSH-2.0-OpenSSH_7.9
debug1: Remote protocol version 2.0, remote software version babeld-849b9b5f
debug1: no match: babeld-849b9b5f
debug1: Authenticating to github.com:22 as 'git'
debug1: SSH2_MSG_KEXINIT sent
debug1: SSH2_MSG_KEXINIT received
debug1: kex: algorithm: curve25519-sha256
debug1: kex: host key algorithm: rsa-sha2-512
debug1: kex: server->client cipher: chacha20-poly1305#openssh.com MAC: <implicit> compression: none
debug1: kex: client->server cipher: chacha20-poly1305#openssh.com MAC: <implicit> compression: none
debug1: expecting SSH2_MSG_KEX_ECDH_REPLY
debug1: Server host key: ssh-rsa SHA256:nThbg6kXUpJWGl7E1IGOCspRomTxdCARLviKw6E5SY8
debug1: Host 'github.com' is known and matches the RSA host key.
debug1: Found key in /Users/myself/.ssh/known_hosts:1
debug1: rekey after 134217728 blocks
debug1: SSH2_MSG_NEWKEYS sent
debug1: expecting SSH2_MSG_NEWKEYS
debug1: SSH2_MSG_NEWKEYS received
debug1: rekey after 134217728 blocks
debug1: Will attempt key: Generated by Sourcetree on macOS for myself-GitHub RSA SHA256:WnUQPEasG3tUVyEkE7Ufo9fGoRqCdUeY9ohZ7OU6fsc agent
debug1: Will attempt key: /Users/myself/.ssh/id_rsa
debug1: Will attempt key: /Users/myself/.ssh/id_dsa
debug1: Will attempt key: /Users/myself/.ssh/id_ecdsa
debug1: Will attempt key: /Users/myself/.ssh/id_ed25519
debug1: Will attempt key: /Users/myself/.ssh/id_xmss
debug1: SSH2_MSG_EXT_INFO received
debug1: kex_input_ext_info: server-sig-algs=<ssh-ed25519,ecdsa-sha2-nistp256,ecdsa-sha2-nistp384,ecdsa-sha2-nistp521,ssh-rsa,rsa-sha2-512,rsa-sha2-256,ssh-dss>
debug1: SSH2_MSG_SERVICE_ACCEPT received
debug1: Authentications that can continue: publickey
debug1: Next authentication method: publickey
debug1: Offering public key: Generated by Sourcetree on macOS for myself-GitHub RSA SHA256:WnUQPEasG3tUVyEkE7Ufo9fGoRqCdUeY9ohZ7OU6fsc agent
debug1: Server accepts key: Generated by Sourcetree on macOS for myself-GitHub RSA SHA256:WnUQPEasG3tUVyEkE7Ufo9fGoRqCdUeY9ohZ7OU6fsc agent
debug1: Authentication succeeded (publickey).
Authenticated to github.com ([140.82.113.4]:22).
debug1: channel 0: new [client-session]
debug1: Entering interactive session.
debug1: pledge: network
debug1: Sending environment.
debug1: Sending env LC_TERMINAL_VERSION = 3.3.8
debug1: Sending env LANG = en_US.UTF-8
debug1: Sending env LC_TERMINAL = iTerm2
debug1: client_input_channel_req: channel 0 rtype exit-status reply 0
Hi myself! You've successfully authenticated, but GitHub does not provide shell access.
debug1: channel 0: free: client-session, nchannels 1
Transferred: sent 3564, received 2484 bytes, in 0.2 seconds
Bytes per second: sent 18846.5, received 13135.4
debug1: Exit status 1
I still can't push code to github despite getting the You've successfully authenticated message in this debug output, the SSH identity being generated by SourceTree itself, and ensuring my SSH Agent is running by doing eval "$(ssh-agent)".
I can also see the expected key in my github profile.
What is wrong here?

Answer 1

my SSH Agent is running by doing eval "$(ssh-agent)".
This is likely the problem. ssh knows to talk to ssh-agent via the SSH_AUTH_SOCK environment variables. Environment variables are only visible to a process and its children.
eval "$(ssh-agent)" sets SSH_AUTH_SOCK for this shell and its children only; that is anything you ran from that shell. If you then run git in this shell it should work. But if you have some stand alone program not launched from this shell, like Atlassian Sourcetree, when it runs ssh it will not know to talk to that ssh-agent.
You could launch Sourcetree from that shell, but that's not a very good solution.
To fix this, and a host of other ssh related problems, start your ssh-agent at login. This should be done for you by your operating system, or if not follow the instructions for your operating system. Otherwise, follow the advice in the various answers here.