2012 XC60 - Fuel gauge readings issue

[hhertz]

Greetings!

I drive a 2012 XC60 T6 AWD R-Design with a reasonable mileage of 60k+. Usually, I put a US Regular gas in it, although Polestar suggests using Premium for "better performance".

Recently, I noticed what seems to be a fuel gauge malfunction.
Basically, I entered a gas pump with about 1/2 a tank and fueled the car up to max, paid something that made sense for half a tank.
Right after I got into the car, I saw that the amount of fuel in the tank is shown as unchanged. After driving for a couple of hours, I watched the fuel lever "progress bar" reach 100%, and then gradually decrease under consumption.

During further "fueling-ups" it feels like sensor is working correctly, but I still keep track of miles traveled as a secondary source of truth.

I requested a quote from a repair shop, and got scared away by a whoping $1.5k for the entire fuel pump replacement.
My question is if it's possible to diagnose myself which part of the system is faulty, and how can repair cost be reduced.

Thanks!