Executing a Google App Script from a Chrome Extension using REST API

Question

I have a Google App Script bounded to a Google doc and deployed as an API executable. This provides me with an API end-point in the following format.

https://script.googleapis.com/v1/scripts/<ScriptId>:run

Now, I want to hit this API from the background.js file in my Chrome Extension project. I'm unable to find a resource which elucidates all the steps required in doing so.

Thus far I have set the project ID equal to the project Id being used for my chrome extension project. I get an OAuth token using chrome.identity.getAuthToken and add it in the header before hitting the API above.

I essentially want the script to return the cursor's surroundTextOffset back to my chrome extension. The script just has one function:

 function myFunction() {
  let cursor = DocumentApp.getActiveDocument().getCursor();
  if(cursor){
    console.log(cursor.getSurroundingTextOffset());
    return cursor.getSurroundingTextOffset();
  }else{
    console.log("cursor", cursor);
  }
}

The API request from my Chrome Extension looks like this:

let fetchIndex = () => {
  chrome.identity.getAuthToken({ interactive: true }, (token) => {
    let init = {
      method: "POST",
      async: true,
      headers: {
        Authorization: "Bearer " + token,
        "Content-Type": "application/json",
      },
      body: JSON.stringify({
        function: "myFunction",
        parameters: [],
        devMode: true,
      }),
    };
    fetch(
      "https://script.googleapis.com/v1/scripts/<ScriptId>:run",
      init
    ).then((response) => {
      return response.json
    }).then((data)=>{console.log("data", data});
  });
};

When I run the the script inside Google's text-editor it runs perfectly and outputs the index position in the console. When I try to make an API hit from background.js via the code above it returns and error object, with the following details

@type: "type.googleapis.com/google.apps.script.v1.ExecutionError"
errorMessage: "TypeError: Cannot read property 'getSurroundingTextOffset' of null"
errorType: "ScriptError"

I suspect there might be an issue with the request's body.