gnupg – Retrieving GPG Private Sub-Key ID

I’ve created a GPG keyring as follows:

pub   rsa4096 2020-09-22 (C)
      CAF532F48781F8A0973317A41F2912156496A89A
uid           (ultimate) Ryan McClue <user@email.com>
sub   rsa4096 2020-09-22 (S) (expires: 2021-09-22)
sub   rsa4096 2020-09-22 (E) (expires: 2021-09-22)
sub   rsa4096 2020-09-22 (A) (expires: 2021-09-22)

I export the relevent keys and copy to an encrypted USB:

gpg --armor --export-secret-subkeys $KEY_ID > private-sub-keys.asc

Now, on a new machine I import these keys and assign ultimate trust:

gpg --import private-sub-keys.asc
gpg --edit-key $KEY_ID

Now as I understand it, GPG stores the public and private keys in the same file (roughly speaking). So the commands gpg --list-keys and gpg --list-secret-keys output only the public key id’s. In wanting to setup git to sign my commits using GPG, i.e. git config user.signingkey how do I get access to my private sub key’s id that is responsible for signing?