Git under nushell not using added ssh-key

I am having trouble setting up nushell in windows 11 to not always ask me for the password for my ssh-key when I am using git.

I have confirmed that ssh-agent is running used ssh-add to add my key and

ssh-add -l

shows that the correct key is indeed added. But whenever I issue a git command that would require ssh, I am asked for my password again.

Any ideas why this might be the case?

Short Version

git config --global core.sshcommand "C:/Windows/System32/OpenSSH/ssh.exe"

More Detail

I was able to reproduce this. It seems that, by default under Nushell:

• In my case, ssh-add (and ssh) in Nushell is coming from the Windows OpenSSH implementation. I'm assuming you have the Windows OpenSSH client installed?

  > which ssh ssh-agent ssh-add 
  ╭───────────┬───────────────────────────────────────────┬──────────╮
  │  command  │                   path                    │   type   │
  ├───────────┼───────────────────────────────────────────┼──────────┤
  │ ssh       │ C:\Windows\System32\OpenSSH\ssh.exe       │ external │
  │ ssh-agent │ C:\Windows\System32\OpenSSH\ssh-agent.exe │ external │
  │ ssh-add   │ C:\Windows\System32\OpenSSH\ssh-add.exe   │ external │
  ╰───────────┴───────────────────────────────────────────┴──────────╯
  

• On the other hand, as far as I can tell, git for Windows seems to default to using the Git-bash provided /usr/bin/ssh. This requires that the environment variables are set properly by /usr/bin/ssh-agent -s (normally eval'd into Bash or other shell). Under Git-Bash:

  $ which ssh ssh-agent ssh-add
  /usr/bin/ssh
  /usr/bin/ssh-agent
  /usr/bin/ssh-add
  

Since the Git-bash /usr/bin/ssh-agent isn't available under Nushell for Windows, we need to config Git to just use the Windows OpenSSH agent directly. This can be done (reference) via:

git config --global core.sshcommand "C:/Windows/System32/OpenSSH/ssh.exe"

After I did that, git under Nushell used my ID to access private GitHub repos.