Back in the day.. Fuel guages were a hot wire movement where the electric current heated a wire in the guage which warmed it up and thus it got longer which was used to move the needle. It takes time to warm the wire so the gauge is said to be damped. You would switch the ignition on and the needle would creep up over a couple of seconds.
Now guages are moving coil and react very quickly.
Guage reading full when empty and empty when full is down to the sender in the tank and idealy should be fixed there.
Modern cars drive the guage as a stepper motor system with all the damping done is software in the ECU.
If you want to try a capacitor then https://cpc.farnell.com/panasonic/eeufm1v102/capacitor-radial-1000uf-35v/dp/CA07431 might work, I have not tried this myself, connect the negative contact to ground and the positive to the wire from the sender to the guage. This can be done on the back of the guage.