How can I use a browser extension’s API within a standard website?

I’m curious about the feasibility of using the browser extension’s API directly from a standard website. Specifically, I want to understand if there’s a way to interact with the browser API from my web page’s JavaScript while complying with all security measures. I have some background in developing extensions, so I’m familiar with content scripts, background scripts, and message passing. Still, I’m unsure if it’s possible and how to apply these concepts in this context. It should be impossible, but asking is better than giving up.

Here are some aspects I’m curious about:

  1. Is it possible for a web page to call a browser API?
  2. Ensure that such interaction complies with browser security policies and respects user privacy. In extensions, this is the role of the manifest.json. Is there any other similar tool for websites?

From my understanding, content scripts might play a role, but I am unclear on how to set this up securely. Can anyone provide insights, examples or prototypes? I’m super curious about them.

To be clear, I’m currently developing an extension, not a website, but I want to explore, go crazy, and see all the possibilities and constraints. Any pointers to relevant, meaningful documentation or information would be greatly appreciated! They should be related to websites, not extensions.