All of the Tutorials out there are for putting Construct 2 games onto Steam using Greenlight. Now it's Steam Direct.
Even though Steam doesn't have Greenlight anymore, do we just upload an EXE like before? Or do we have to include the full files? Because they're pretty sizeable.
There is no difference to how you upload the games on Steam, the difference between Greenlight and Direct is about games being approved.
You need to include all files required for your game to run, not just the nw.exe, but there are ways to wrap it into a single exe - see this post from TheRealDannyyy
And you say sizeable, but remember there are games that take multiple gigabytes already on Steam, so size doesn't matter unless you've got really bad internet and are worried about upload speeds.
Sign up to Steamworks and start reading through the documentation, it should help clear up a few things. You'll need to do this before going through Steam Direct anyway.