This action currently queries all open issues when looking for stale issues:

https://github.com/actions/stale/blob/main/src/classes/issues-processor.ts#L564

This exhausts the number of github operations for larger repos (we currently have ~7k open issues). I believe this could be made more efficient by qualifying the query (this.client.rest.issues.listForRepo(...)) with the 'stale' label.