I think what you’re talking about doing is quite difficult, and there will be a lot of obstacles in your way. You’re proposing:
Circumventing the API fees, which is something that ChatGPT would definitely not like, and they will make it as difficult as possible. You’re not the only one trying to avoid paying for this very popular service.
Crawling the entire contents of each page with a bot, which is another thing that websites do NOT want you to do. There are only a handful of RSS readers that do this, and they’re paid, closed-source, proprietary apps. And even those probably don’t work on certain websites.
I’m not saying it’s impossible, just that you have chosen a very difficult path here. If you’ve never developed an app before, start with a smaller, simpler project.