The problem with ntfy for me is that I get notifications on my mobile through the ntfy app. On desktop, in the browser (Safari on Mac), I only get notification pop-ups when the website is open.

The worst part is that I don’t even see the notifications on the website that I received on my mobile while the website wasn’t open.

Go to ntfy.sh/settings and enable background notifications. Or do it like I do it an pin the tab and just leave it open.

Unless you have a pro account, notifications are only cached on the server for 12h so that's why you may miss old notifications.