Better options:

c) use proxyjump (-J) to access bar (https://www.man7.org/linux/man-pages/man1/ssh.1.html), and/or

d) generate a new private key on foo and use that to access github.

You might think that's a crazy waste of time compared to forwarding, but it's actually much, much safer and actually only takes a moment:

    ssh-keygen -t ed25519
    cat ~/.ssh/id_ed25519.pub

and then just paste that in Github.

See also https://userify.com/docs/jumpbox for more jumpbox docs.