You would have to pass the value inside the embedding code itself. This is a sample embed code of a form:
<iframe id="miniExtIframe-jV8YFoL846PqKq48Uxxl" height="800" src="https://web.miniextensions.com/jV8YFoL846PqKq48Uxxl"></iframe><script id="embed-script-id" type="text/javascript" src="https://web.miniextensions.com/statics/embed.js?miniExtIframeId=miniExtIframe-jV8YFoL846PqKq48Uxxl"></script>
You will see the URL of the form in the first src parameter in the embed code. You have to append the prefill in this parameter.
On the legacy site app.miniextensions.com
You would need to use the prefilling option in the embedding settings. It's not possible to pass a prefilled value from the page URL to the embedded form.
In order to prefill a form inside of an embed, add the prefill where the screenshot is highlighted, and then you'll need to copy the script again and paste it again on your website.