feat(dev-infra): create caretaker handoff assistant to update github team membership (#42859)

Create a handoff assistant, currently only assists in updating github team membership
for caretaking team.

PR Close #42859

dev-infra/utils/git/github.ts

@@ -45,6 +45,7 @@ export class GithubClient {
   readonly issues = this._octokit.issues;
   readonly git = this._octokit.git;
   readonly rateLimit = this._octokit.rateLimit;
+  readonly teams = this._octokit.teams;
 
   // Note: These are properties from `Octokit` that are brought in by optional plugins.
   // TypeScript requires us to provide an explicit type for these.