First split screen only works in landscape mode, not portrait. There three ways to achieve this.
Open a new tab is split screen
Tap and hold the the tab management icon in the upper right. You will see an option to Open Split View. Tap it to create a blank Safari window.
Open a link in split view
Tap and hold a link on a web page and select Open in Split View.
Drag a tab to open in Split View.
Tap and hold a tab, then drag it to the side of the screen you want it to open in.