Embedding Microsoft Forms with "Only people in my organization can respond" set: works in Chrome, but not in Safari and others

Question

I have a Microsoft Form, where Only people in my organization can respond.

Now I want to embed this form via the embed link in a webpage, that is accessible for people in my organization.

In Chrome, that works just fine. But in Safari and other browsers only this shows up:

What can I do, to show the form directly in all browsers? Does it have to do with the authentication of users in my webpage? Anything I need to send along with the embed-URL?

Thanks in advance