Trigger various cache affecting calls asyncronously

Many calls are cached for two reasons:

1. To mitigate bumping into the GitHub API rate limit
2. To make this application feel "snappier" since some calls can be very time consuming for larger orgs.

This isn't necessarily a v1 requirement, but certain calls (i.e., listing members of an org) NEED to be ran in the background on some set cadence (even when this hooks into GitHub events- we need to validate at some point that no event was missed, after all).

まず、キャッシュされた GitHub 呼び出し、特に組織メンバーの一覧取得と、GitHub イベント処理の経路を特定します。必要な呼び出しが定義された間隔でバックグラウンド実行され、イベント駆動の経路がイベントの取りこぼしを検出できれば完了です。

索引モデルが issue の本文から書いたものです。