ntfy/docs/subscribe/web.md

Subscribe from the Web UI

You can use the Web UI to subscribe to topics as well. If you do, and you keep the website open, notifications will pop up as desktop notifications. Simply type in the topic name and click the Subscribe button. The browser will keep a connection open and listen for incoming notifications.

To learn how to send messages, check out the publishing page.

To keep receiving desktop notifications from ntfy, you need to keep the website open. What I do, and what I highly recommend, is to pin the tab so that it's always open, but sort of out of the way:

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Pin web app to move it out of the way