Scheduled Event Processor failing to add "no-recent-activity" label.

While investigating why https://github.com/Azure/azure-sdk-for-net/pull/51992 was not closed it appears as though there is an error processing when trying to add "no-recent-activity" label which explains why we never clean-up.

https://github.com/Azure/azure-sdk-for-net/actions/runs/20360467308/job/58504715214

```
UpdateGitHubIssue:ApiValidationException processing IssueUpdate on 51992. ApiValidationException=Octokit.ApiValidationException: Validation Failed
at Octokit.Connection.HandleErrors(IResponse response) in /_/Octokit/Http/Connection.cs:line 785
at Octokit.Connection.RunRequest(IRequest request, CancellationToken cancellationToken, Func`2 preprocessResponseBody) in /_/Octokit/Http/Connection.cs:line 766
at Octokit.Connection.Run[T](IRequest request, CancellationToken cancellationToken, Func`2 preprocessResponseBody) in /_/Octokit/Http/Connection.cs:line 751
at Octokit.ApiConnection.Patch[T](Uri uri, Object data)
at Azure.Sdk.Tools.GitHubEventProcessor.GitHubEventClient.UpdateGitHubIssue(GitHubIssueToUpdate issueToUpdate) in /mnt/vss/_work/1/s/tools/github-event-processor/Azure.Sdk.Tools.GitHubEventProcessor/GitHubEventClient.cs:line 441
{"message":"Validation Failed","errors":[{"value":"Copilot","resource":"Issue","field":"assignees","code":"invalid"}],"documentation_url":"https://docs.github.com/rest/issues/issues#update-an-issue","status":"422"}
```