You may refer to the Go “Release History” page: “each major Go release is supported until there are two newer major releases. For example, Go 1.5 was supported until the Go 1.7 release, and Go 1.6 was supported until the Go 1.8 release”.
Currently, App Engine First Generation runtime supports Go version 1.11. According to Google Cloud Platform Services Subject to the Deprecation Policy: "Google App Engine development and deployment tool support for a programming language version that is no longer publicly supported by, or receiving security updates from, the organization maintaining that programming language".
Go 1.9 deprecation was announced on the Feature Deprecation page. It should be noted that the message you received is not asking you to migrate all your apps by October 1, rather to upgrade the Go runtime environment in the First Generation runtime from version 1.9 to 1.11 before October 1, 2019.