Incognito / Private Browsing Mode: Chrome, Firefox, and Safari do not offer support web push notifications in incognito / private browsing, in order to protect the privacy of their users.
You can see the difference between normal browsing and incognito mode below.
In-app browsers (Facebook, Instagram, Twitter, etc.): When you open a link on a social media platform like Facebook, the webpage opens on the app's native browser. Since most of these in-app browsers are not based on Chrome WebView, visitors can't subscribe to the store notifications, and so, they don't receive push notifications either.