Codes P2097 and P0171?

Hello, yes unfortunately when a vehicle is over filled like this, liquid gas gets into the Evap system which is only designed to pull gas vapor from the tank. Most likely what happened is there is gas inside the charcoal canister now, and it has either broken apart and caused the Evap Purge valve to stick open, or it is drawing liquid gas in through the Purge valve, or both. Causing a rich code to appear, but also since the Vent valve is open during normal operation, its pulling oxygen through the Evap system and having a rich, lean back and forth effect. The handles at the gas pump click off when the tank is at its max. When people unknowingly pull the handle out further it fills up the filler neck and causes the Evap problem. So the P2097 post Catalyst Rich bank 1 code is setting due to the rear oxygen sensor detecting too much fuel. And possibly the Purge valve being stuck open when it shouldnt be can be causing the P0171 which is a lean exhaust code.
It can be confusing seeing a rich and lean code at the same time, but thats how it can happen. With this being a semi more modern vehicle, Im sure it has a much more up to date type of Evap system with much stricter monitors watching for emissions.
You can pull the Purge valve off and see if it is stuck open, or if there are any Charcoal particles stuck in it. But the Evap Charcoal canister will have to be checked to see if its full of gas and that it did not break apart inside.
You can try erasing the codes and see what comes back. It might be able to recover once some of the fuel level goes down, but the canister usually has issues after something like this. I also see the P2097 code is set when the system fails 2 drive cycles, there is a very extensive flow chart for this code, but since you know already what happened theres no need to go through it all.
I see a pretty technical setup in the wiring diagrams, there are 2 different designs, one system has 2 Purge valves near the Intake manifold and the other has just 1.
And the Charcoal canister is in the rear on the vehicle near the gas tank. Ill post some diagrams of the Purge solenoids in the engine compartment.

Diagrams 1-6 are for a system with 2 Purge valves, diagram 3, step 3 requires the vacuum pump to be removed. Diagrams 5,6 are for removing the vacuum pump to access both purge valves.
Diagrams 7,8 are for the system with 1 Purge valve. Since it's a Bank 1 code, it might be just one of the Purge valves that may be stuck open on the dual system.
Getting to the Charcoal canister is very extensive, it requires removing the rear section of the exhaust, removing the rear drive shaft, and lowering the rear differential. This would require a lift to get the vehicle up in the air.

Here's a guide that explains the Evap/Emissions system a bit more:

https://www.2carpros.com/articles/how-emission-control-systems-work

It would be good to take the valve or valves off and inspect them to verify that is the issue. Do the diagrams make enough sense to find the valves (solenoids)? According to service info, the system that has 2 Purge valves, they have different size openings. So, it looks like one Purge valve will flow a bit more than the other one. I think that you will find one valve is stuck open partially.

If you take them or the one off, depending on the setup, you should not be able to blow air through the valve, it might flow air in the opposite direction. I have seen that on certain Purge valves before, but when off the vehicle it should not allow any air to be pushed or pulled through the valve.

This system works with the Intake manifold's vacuum, which is at its strongest pull at idle with the throttle plates closed (so foot off the gas pedal). I worked for Subaru in the early 2000's, so if you don't understand where the valves are located, I can try to explain it a little better. These engines are pretty easy to understand, since almost all the sensors and electrical components are on top of the engine.

The setup with 2 Purge valves does have you move the vacuum pump, but that is only 2 bolts holding it on. Then the bracket for the vacuum pump is bolted to the Alternator with 2 more bolts. And then you'll have access to the Purge valve on that side.

I'd like to know if one of them is sticking open, and if it has any charcoal from the Canister in it. I didn't not see many of these valves go bad in all the time I was there. We need to know if there is any charcoal in the valve, which means that the charcoal in the canister did get broken up somewhat and this can cause any new Purge valves to fail prematurely. So, if an overfill of the gas tank caused this, I think it did. It would be good to know, and this will help out future customers with this year Subaru. Since it is a more modern design.

The code took a couple of days to set because the engine computer will need to see the fault occur at certain amount of Key cycles or drive cycles before setting any fault codes.
And on a side note, it looks like the system with 2 Purge valves might be the (H4DOTC) engine with a Turbo. The other is the (H4DO) engine without a Turbo. The diagram below is a better view of where the 1st valve is located, you'll notice the vacuum hose marked in green, that runs to the Intake manifold.
The 2nd diagram shows the air flow test and the two different sizes of the valves on the Turbo setup. I'm surprised that no Fuel Tank pressure sensor codes have not set, but that might happen once this lean condition is repaired. The pressure sensor is usually at the top of the gas tank, or on the Evap vapor hose running to the engine.

Let me know if you have any questions at all.

Is the code still setting?

According to that VIN number it looks like your vehicle only has 1 Purge valve, and that part number you have there is the entire leak detection pressure sensor and switching valve. Are you getting the P0171 code stored only? If it's just the P0171 lean exhaust code I would check the Purge valve being stuck open first before replacing that entire assembly.
This 1st diagram is looking directly at the front of the engine, remove the engine cover first and you'll see the purge valve. I colored in blue in the first diagram. It's very easy to find.

Okay, then you're getting an air leak somewhere, and that can happen if the purge is sticking open. If there were any other issues with the Evap system, you would be getting codes for that. Let me know what you find.

I'll verify that part number for you, this is the 2.5liter engine, correct?

This is the 2.5liter engine correct?

If this is the Non-Turbo 2.5 liter then yes that's the correct part number. The 2.0 liter engine has a Turbo and uses the 2 Purge valve system.