How do i know if the battery is fully charged 12volt peg Perego battery

They won't work with a Lithium battery. The controller circuitry doesn't understand this weird new battery. They don't work on electric kiddy bikes without changing the controller and then not all work as expected. They also don't work on full size motorcycles as a starting battery.

Upgrade Kids John Deere Tractor Battery in Peg Perego ...

Impact Battery https://www.impactbattery.com > blog > post > upgrad...
Aug 24, 2021 - Learn how to replace your kids John Deere tractor battery and extend ride time by installing the new 12V 15Ah Peg Perego battery upgrade.

.

Maybe the gears inside it are worn down or off kilter?

did you verify the battery voltage with a multimeter, could have a bad charger that gives a green light making one think that the battery is fully charged, also check the fuse on the battery

have you verified that your charger is putting out between 13.8 and 14.6 volts?

nope wait until the light turns green again, then its fully charged

check the charger with a multimeter and the battery and make sure that they are showing 24 volts

yep its just has longer capacity

Normally, you would need to charge overnight- 12 hours.

I would replace the high/low switch and the reverse switch.
You can get the peg perego parts at http://www.shopjandl.com/
but I would first check the connections on the motors and foot switch. Sometimes they come loose.
Hope this helps

The green light means it is ready to use. If the battery is bad though, the light will still be green.