I ALWAYS use browsers. There is no reason to use an app if there's a browser, especially if you use firefox/forks because you can download the webapp onto your home screen and its a web page that works just like an app.
As far as fingerprinting and cookies, I have a dedicated browser for a lot of things. For normal online shopping, banking, amazon, etc, I use Firefox. For buying guns/accessories, browsing forums, etc, I use brave. I also use mullbrowser for webapps.
Hope this helps