Shuffle libs private channels

[clarfonthey]

Needs coordination from a Zulip admin. Basically:

• Current #t-libs/private channel is occupied by the old libs + libs-api team, and does not track the new libs-fcp team. The intent was to remove it, but we didn't want to block the team refactor on doing this, since we were preoccupied with crate ownership.
• Current #t-libs/reviewers channel is occupied by the new libs team.

The goal:

• Archive the old t-libs/private channel and name it something like t-libs/private-archive (I don't know how this has been done in general)
• Rename t-libs/reviewers to t-libs/private

Old message clarifying this was okay: #2651 (comment)

[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
[INFO  rust_team::sync] 💻 Repo Diffs:
    📝 Editing repo 'rust-lang/rustup-components-history':
      Environments:
        🔄 Update: github-pages
            Removing branches: main