Websites usually link to their RSS feed using a <link> attribute in the head of the page.

Browsers used to detect this and show an RSS icon near the address bar if the website you were viewing had a feed - and you could click the icon to see more details and subscribe.

I use this Firefox addon which replicates that functionality: https://addons.mozilla.org/en-GB/firefox/addon/feed-preview/

FreshRSS is a good self-hosted RSS feed reader, and you can configure it to scrape non-RSS webpages for updates too: https://danq.me/2022/09/27/freshrss-xpath/

Great tip on the <link>, thanks a lot! Also the pointer to FreshRSS, I might end up running an instance of that in our basement.