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.

[marcoieni]

Sorry I didn't have time to look into this. I'm unassigning this from me because I'm going to rustconf and after that I'll be on PTO for two weeks.
Hopefully someone else has time to look into it!