I have a suggestion. Since 'power factor' is an issue with some inverters powering supplies that are themselves switching voltage converters/inverters, I recomend you add another moderate load to the inverter when the e-bike charger is operating.
Not a large, heavy load, but one that is resistive as much as possible.
If you have a 50-100 watt incandesent-bulb lamp, a soldering iron, an electric blanket, electric heating pad, etc, try one of those.
Failing that, try something else that is motorized, but not electronic, such as that blender or an electric drill.
It's complex to explain 'power factor' but in simple terms, the e-bike charger may not be presenting the inverter with a load that it is happy with. Adding a more resistive load to the inverter at the same time might even things out.
Residential (grid) AC power is much more forgiving of weird or low power factor devices than some off-the-shelf inverters.
Of course, this does not 'fix' the 3A charger, but would explain the issues you are having.