Apple released Safari 16.1 today. Here are the standalone installer links from Apple's SUS catalog for anyone needing to make these updates available via Self Service:

Safari 16.1 for macOS Monterey: https://swcdn.apple.com/content/downloads/04/41/012-89022-A_0O25N5267C/8vvwcsyap2nweiiv95zrqleofs2283yaa2/Safari16.1MontereyAuto.pkg

Safari 16.1 for macOS Big Sur: http://swcdn.apple.com/content/downloads/06/51/012-26885-A_XE7OL6TYXT/3di69zxamb1frajv1zf4dnei1jaz0765vn/Safari16.1BigSurAuto.pkg

(There is no Safari 16.1 installer for macOS Catalina or earlier)