Here are a few things to try when notifications are not working in Safari on an iPhone. Work through them in the order given to make sure notifications behave as they should.
Fix 1: Check your iOS version
Make sure your iPhone is running the latest available version of iOS. Go to Settings -> General -> Software Update to check for and install any updates that are available.
Fix 2: Check whether Focus mode is switched on
Check whether Focus mode (do not disturb) is switched on, as it can block notifications. Go to Settings -> Focus and make sure no Focus mode (Do Not Disturb, for example) is active.
Fix 3: Check the app notification settings for Assist
Go to Settings -> Apps -> Assist to confirm that all notifications are switched on for the app. Make sure that Allow Notifications is on and that every relevant notification type is enabled.
Fix 4: Clear history and website data in Safari
If notifications still do not work, this may be a known Safari bug where it incorrectly remembers GPS and notification permissions. Clearing the Safari history resolves it. Go to Settings -> Apps -> Safari, tap Clear History and Website Data, then choose All history to complete the reset.