What part does a capacitor play on a Coleman generator. Teapo 130mf 200v

What does a teapo capacitor 130 microfarad 200 volts play in a Coleman generator

More than likely its either part of the exciter circuit or the voltage regulator circuit depending on why type of generator voltage regulation method they are using.

I would replace it.
A wifi router I was using a number of years ago had a bulged Teapo cap, which stopped it working.
Once replaced, the router was fine again.
Even if it has not bulged and vented, it is probably high ESR by now if there's any heat around it.