If you want to use a plain javascript API, there is a good example at https://github.com/hongkiat/js-rss-reader/
The complete description at https://www.hongkiat.com/blog/rss-reader-in-javascript/
It uses fetch method as a global method that asynchronously fetches a resource. Below is a snap of code:
fetch(websiteUrl).then((res) => { res.text().then((htmlTxt) => { var domParser = new DOMParser() let doc = domParser.parseFromString(htmlTxt, 'text/html') var feedUrl = doc.querySelector('link[type="application/rss+xml"]').href })}).catch(() => console.error('Error in fetching the website'))