Does this violate electrical code? (UF run plugged into GFCI to use smart outlet)

I agree, this is "nope".

The way I would handle this - first, I'd use metal boxes because I'm lazy about running ground wires.

I'd start by removing the current box. I'd knock out the highest 1/2" or 3/4" knockout and fit an EMT spacer to connect to a 4-11/16" square steel box. We'll need the room. Fit a steel cover that provides 2 Decora. One slot gets the GFCI outlet. The other slot gets a 15A inlet.

Both cables to outside terminate in the box. I'm moving the box upward to create some slack so you can deal with codevio's at the window entrance.

The cable you want switched goes to the inlet. The cable that is not switched goes to the GFCI's LOAD terminals. The GFCI LINE terminals go to white and black wires, which run through to the panel to the breaker and neutral bar.

Then you plug the smart switch into the GFCI. Then you use a 1' long extension cord to go from the smart switch to the inlet.

The grounds for the inlet and cables get pigtailed to the ground screw in the box. The box and the close nipple carry ground to the service panel and outlet.

That cable near the window is vulnerable to physical damage. It should be folded down more tight to the wall, and guarded by something, not least so the window-opening mechanism can operate without endangering the cable.

A plug-in smart outlet is the wrong device for this

Instead, what you want is a smart relay, or smart light switch. That way, you can wire directly off the load side of your GFCI, and will not need a creative solution to connect the output of a NEMA 5-15 socket into your fixed building wiring.

Option 1: UL Listed Smart Relay

Although specific product recommendations are off-topic for this site, I'm going to link to one anyway, since as far as I know, there's only one smart relay module that's both UL listed and compatible with modern smart home systems (Alexa/Google Home): The Shelly 2.5. Note that they currently sell them in both UL listed and non-listed versions -- if you're in the US, you need the UL listing to be legal and pass inspection; if you're in Europe, you can use either. These are designed to mount in a junction box or on a DIN rail.

Option 2: Smart Light Switch

Here, you have more options from all the usual suspects (Lutron, GE, etc). Note that you'll still want to look for a UL listing. Replace the junction box your GFCI is in with a 2-gang one, and add a smart switch next to the GFCI. Wire the line side of the smart switch to the load side of the GFCI, and the load side of the smart switch to the UF cable feeding your outdoor outlet. An advantage of this setup is that you can manually operate the switch even if your wifi goes down.

My actual solution

I fixed this a while ago but never came back to update the post. I ended up getting a Wemo smart light switch (since I already have other Wemo devices) and wired that to the load side of my GFCI to control my outside outlet. Looks nice and works great!