Do battery connectors handle more amperage than the charger port?
Yes, it is safe to assume that the maximum current rating of the connectors is considerably higher than the typical/max. current they will carry.

Sometimes this is because of derating, whereby components rating exceed maximum stress in circuit by a standard margin. The standard may be a company standard, military/avionics/etc standard or just the personal good practice of the design engineer.

Sometimes it's because the standard connector for the application gives you more than you need. This is true of mains plugs, which in the UK are fused at 13 A and capable of more but where the vast majority carry less than 5 A. All those TVs, phone chargers and lamps and so few kettles and vacuum cleaners...

And sometimes it's because the mechanical requirements of the application require larger metal connectors. This is true of a PP3 battery connector, which has much larger conductors than the practical drawn current of the 9 V battery needs.

Of course, a percentage of the equipment around will be badly designed and not follow these rules. But you're quite unlikely to bump into that stuff that often.