No edit button in Safari

The Edit button is not at the bottom of the tabs screen, its at the bottom of the new Tab you just opened.

Below Favorites, Frequently Visited, Reading List etc... in that screen, scroll to the very bottom of the new tab.

click here ➜ Customize your Safari settings on iPhone - Apple Support

Well that's very strange.

Have you tried force closing Safari and restarting the iPhone.

click here ➜ Close an app on your iPhone or iPod touch - Apple Support

then here ➜ Restart your iPhone - Apple Support

Are you sure you are opening a new tab?

Tap on the 2 squares icon, and then on the + icon to open a new tab.