GVWR for your vehicle refers to what the vehicle is carrying. It is not specific to towing. It is the actual weight of the vehicle and everything in or on the vehicle that the vehicle is supporting on it's tires and suspension. It includes all of your cargo, all of your passengers, and (if you are towing) the tongue weight of the trailer.
GVWR for the trailer would be the weight of the trailer, the boat, engine, fuel, and everything else in the boat. Again, it is a maximum that the suspension and tires can safely tow.
GAWR is the maximum weight that can be placed on each axle. It is often different between the front and the rear axle. The numbers will often be different between the front and rear axle and will certainly be different between the vehicle and the trailer axle.
tldr: GVWR is maximum weight allowed on the suspension of the vehicle or the trailer. GAWR is how the weight is distributed between the axles.
The towing capacity listed by the manufacturer has some assumptions and tends to be influenced by marketing. It's best not to get too close to it unless you are dealing with a vehicle that was designed with towing in mind. The average passenger car or light SUV does not meet that definition. The towing capacity usually accounts for the curb weight of the vehicle and the driver. Nothing else.
I have no idea where the service person you spoke with came up with the "count everything else and multiply by 10" rule. Maybe I'm extra dense tonight (this morning) but I can't make any sense out of it.
In general in your particular case here's how I would figure it.
Assuming worst case and you are going to load the trailer to the max you will be pulling 4200 pounds. The 4200 pounds the maximum weight that the trailer can carry on its suspension. For the purposes of this example I'm just assuming that you have maxed out the trailer without knowing how it is distributed. Note that North Carolina requires brakes on boat trailers over 4000 pounds.
I have an X, an aluminum trailer, and a Honda 40 (same weight). With trailer, boat, batteries, fuel, and engine I'm at 3655 pounds. It does not take much gear in the boat to get
well north of 4000 pounds being pulled.
Assuming your tongue weight will be approximately 10% of your trailer weight. That's the equivalent of 420 pounds of cargo.
GVWR of your vehicle is 5622 pounds.
Curb weight is 4101 pounds. Curb weight includes all fluids and standard equipment is present but no passengers or cargo.
5622 - 4101 = 1521 pounds for passengers and cargo.
1521 - 420 = 1101 pounds left after trailer is attached.
Best case you have 1101 pounds available in the vehicle for people and gear. It is possible that the number is lower due to GAWR constraints but I have no way of knowing how you will be loading the vehicle.
I don't want to scare you or try to get you to buy a new tow beast. I knew someone in southern Georgia who pulled his "M" with a Dodge Caravan. I don't know how he ever got it back up a ramp.

The numbers for your Kia are not much different that they were for the first vehicle I used to pull my "X". Who am I kidding, yours are a bit better. It was a borderline call and I probably abused the suspension but it survived. If you are not pulling it very far and you are not pulling it in the mountains you probably won't have issues.