How do I do this in Blender?

How do I scale a face like this so I can extrude a smaller piece out?

Select the face, press E then press S and move the mouse or type the value and press ENTER/Left Click once done.
(Unfortunately, unlike in the gif, Blender is not be able to keep the UV and texture that nicely during those operations)
Then press E and extrude up

An alternative would be to select the face, press I to inset,
(there it will keep the UV/texture nicely)
and then select the smaller face, then press E and extrude up
(unfortunately as soon as you extrude, uv/texture will go bad even with live unwrap enabled)

When I press S after E on a face it doesn’t do anything, but using I works for me. Thanks!

Press E, then hit enter, then hit S. That’ll give you what you are looking for.