No, there is no way to switch full screen mode in Safari on iOS using javascript.
For the web page to start in full screen mode, you need to add the following meta tag, and the page must be launched from a bookmark on the main screen:
<meta name="apple-mobile-web-app-capable" content="yes">
However, you can determine if the page is working in full screen mode or not using javascript using the read-only property:
window.navigator.standalone
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