Gas gauge took a long time to mark full?

Hello everyone! I hope you are doing well. I was filling up my tank this morning, and ran into a bit of an issue that’s never happened.

I filled up my tank, and the gas nozzle automatically shut off, which usually means the tank is full right? Well when I got into my car,the gas gauge was one “tick” away from being full, suggesting that the tank is not completly full. However, I drove the car for about 15 minutes, and when I pulled into the parking lot, I noticed that in that 15 minutes, the gauged “reached” full. Basically it took 15 minutes to reach the “full” mark.

Does anyone know if there could potentially be a larger issue at hand? I realize this seems like essentially a “cosmetic” issue, but with the car being old already and me not being the most knowledgeable about cars in general, anytime something goes wrong, I worry there could potentially be a larger can of worms in terms of potential repairs. Thank you for your assistance!