How long does it take this modern fuel to go bad?

Last time I filled my tank with shell 87 was early June.
Have not been driving much but start it and drive a little last three months.
I have less than 1/4 tank left.
Other day the truck started to die at idle.

Check carb (Carter 787s) I no longer get a squirt in throat when I hit accelerator pump.

Pulled new sender in new tank. The gas is a dark honey color, gas bowl fuel pump is same color.

Gas in the tank has a sheen or film on it.
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1, Can this modern fuel go bad in just 3 months?
2, Can I just add fresh fuel and mix?
3, Rebuild carb? If it’s not bad gas what else should I look for.
Thank you