Pulumi utilizes GitHub for its development process, employing topic branches that are often forgotten and left undeleted after merging pull requests. To address this, Pulumi employs automation through serverless functions and webhooks, leveraging GitHub's webhooks and Pulumi's serverless capabilities to automatically delete branches post-merge. By creating an HTTP endpoint that listens for GitHub events, Pulumi can log events and validate webhooks using HMAC signatures. Pulumi further enhances this process by using dynamic resources to streamline webhook registration and management with GitHub, allowing the automation of tasks such as deleting merged branches through tools like @octokit/rest. This integration is encapsulated in a GitHubWebhook component, which abstracts the complexities of managing webhooks and integrates the registration process as a resource within Pulumi's infrastructure, showcasing Pulumi's flexibility in extending and sharing such abstractions through packages.