Added org github tokens to check untracked private repositories

[cuba0001]

Related #2654

[github-actions]

Dry-run check results

[WARN  rust_team::sync] sync-team is running in dry mode, no changes will be applied.
[INFO  rust_team::sync] synchronizing crates-io
[INFO  rust_team::sync] synchronizing github

[marcoieni]

We already parse and select GITHUB_TOKEN_{ORG} credentials in

team/src/sync/github/api/tokens.rs

Line 194 in 0a7e85b

fn org_name_from_env_var(env_var: &str) -> Option<String> {

Could we reuse that mechanism here?

[cuba0001]

It was a bit tricky because of two github clients. I needed to expose tokens.rs to reuse it in api/github.

[rustbot]

This PR was rebased onto a different main commit. Here's a range-diff highlighting what actually changed.

Rebasing is a normal part of keeping PRs up to date, so no action is needed—this note is just to help reviewers.