What is the correct direction for hot on a vertical single handle faucet?
You've found one of the major conundrums of modern plumbing.
In the US it has always been hot on the left and cold on the right. Europe - I'm not sure about.
However, as faucet design has changed it's become complicated as you pointed out. This started with single lever faucets, which was okay, because left was still hot and right cold. But then they started putting them on the side. When they went to the side, and even before that, many manufacturers started marking them - hot &amp; cold but some didn't.
Now to your dilemma. If the faucets are unmarked you can set them up however it suits you. I'm not aware of any codes dictating that.
My preference when a single lever faucet moves either toward you or away is to have the cold toward and hot away. I think this works best with small children because they have a hard time reaching them and it's easier to pull than push away - thus cold forward.
The main thing is to get them the same throughout your house so there's no confusion. Since neither has an indicator I would change the Delta in the bathroom so that hot is back toward the wall. It's easy enough - just swap the supply lines under the sink. The good thing is whichever way you put them people will adjust quickly.
First Edit
What Ed Beal is saying in his comments is correct. If you think about rotating the handle left even if it's front to back, that left would be hot and right would be cold. I don't think code requires that on the type of setup you're asking about - but Ed Beal would know. In that case you would want to swap the supply lines under your kitchen sink instead of the bathroom.
Importantly, you want them the same.