In a post to his site Freek van Der Herten shares some functionality that Spatie uses to help keep the stale pull requests under control across their 180+ repositories: a Botman-based bot that assesses the last updated date and closes after a given amount of time.

At Spatie we have over 180 public repositories. Some of our packages have become quite popular. We're very grateful that many of our users open up issues and PRs to ask questions, notify us of problems and try to solve those problems, ...

Most of these issues and PRs are handled by our team. But sometimes those issues and PRs become stale. [...] That's why we created a bot that can automatically close stale issues and PRs. Here's [an example] of the bot in action.

He then shares the code they currently use for the bot, making use of the BotMan package as a base and the knp-labs/github-api package for the GitHub interaction. The code includes the GitHub service provider, a client class, an Issue object and the command that's run to find and close out the stale pull requests and issues.