In order to be able to send a photo via sendPhoto method, you have to send a proper picture file or a string represent a valid URL.

According to code you posted, you're sending into the HTTP request as body parameters the chat_id, the text message itself and that's it.

The sendPhoto method does not expect a text field, that's used in sendMessage method.

In your case, since you're trying to send via Telegram chatbot a picture taken from the HTML entity, which in this case is not the picture itself but its path on your webserver, you have to change the POST request body and to set the picture URL as parameter of the request itself.

To conclude, if you want to add the text message, the sendPhoto method allows you to add it but as caption.

For instance:

var telegram_bot_id = "api";
var chat_id = "id";
var img;
var ready = function () {    
    img = "http://your-website.com/imagepath/imagename.png";

};
var sender = function () {
    ready();
    var settings = {
        "async": true,
        "crossDomain": true,
        "url": "https://api.telegram.org/bot" + telegram_bot_id + "/sendPhoto",
        "method": "POST",
        "headers": {
            "Content-Type": "application/json",
            "cache-control": "no-cache"
        },
        "data": JSON.stringify({
            "chat_id": chat_id,
            "photo": img,
            "caption": message

        })
    };
    $.ajax(settings).done(function (response) {
        console.log(response);
    
        window.location.href = "index.html";
    });

    return false;
    
};