How can I take a larger screenshot on my iPhone?
Natively available in iOS 13 and later
This functionality is now built into iOS 13 by Apple. Safari running in iOS 13 lets you screenshot the entire webpage as a single continuous image.
To do that, open the desired webpage in Safari, and simply take a screenshot as you would normally do on your device, and tap on the thumbnail shown immediately shown towards the bottom left.
You'll be presented with two options at the top in a segmented control:

Screen
and

Full Page


 
With the Full Page item selected, tap on the Share icon in the top right to share the capture via desired medium. AirDropping it for instance, exports a single PDF file, which can be easily exported into a desired image format.