Let's say the git log command returns something like this. Notice in this example that the latest commit has SHA-1 mks910122020slsmm3lsosos020399489sl.

commit  mks910122020slsmm3lsosos020399489sl
Author: Jack Doe <jack.doe@example.com>
Date:   Wed May 31 14:51:14 2020 -0500
  Third commit
commit dkci85474fjfdkd9393934k49f9fk002kd01
Author: Jane Doe <jane.doe@example.com>
Date:   Tue May 30 18:23:36 2020 -0500
  Second commit
commit fj83m3ld0d0d3m3ld0389303l3ld0d0d39dl
Author: John Doe <john.doe@example.com>
Date:   Mon May 29 20:26:09 2020 -0500
  First commit

And .git/refs/heads/<default branch name> should contain the SHA-1 of the latest commit.

~]$ cat .git/refs/heads/main
mks910122020slsmm3lsosos020399489sl

Here is an example of how to list the references using curl.

curl \
--request GET \
--location \
--header "Accept: application/vnd.github+json" \
--header "Authorization: Bearer <your token>" \
--header "X-GitHub-Api-Version: 2022-11-28" \
--url "https://api.github.com/repos/<owner>/<repo>/git/ref/heads/<default branch name>"

For example.

curl \
--request GET \
--location \
--header "Accept: application/vnd.github+json" \
--header "Authorization: Bearer abc123" \
--header "X-GitHub-Api-Version: 2022-11-28" \
--url "https://api.github.com/repos/foo/bar/git/ref/heads/main"

Something like this should be returned.

{
  "ref": "refs/heads/main",
  "node_id": "REF_kwDONtYRc69yZWZzL2hlYWRzL21haW4",
  "url": "https://api.github.com/repos/foo/bar/git/refs/heads/main",
  "object": {
    "sha": "mks910122020slsmm3lsosos020399489sl",
    "type": "commit",
    "url": "https://api.github.com/repos/foo/bar/git/commits/70da4f4e1b9011c1ae50c7ce2ab4ea1af34c0e43"
  }
}