Did I do something wrong? ... I'm using is an IEC320-C13 & 14.
You chose the wrong connectors: they are for AC power, and someone will mis-plug them and cause damage.
Select instead battery connectors.
For interior use (inside the bike, not accessible by the end-user):
MANUF. - SERIES
Amass - MR30
Amass - MR60
JST - RCY
Between the answers and comments, you should have everything you need but let me try and be more direct on the issue with what you are proposing. And I understand why you are pursuing this, simply by reading the high level verbal specifications, it seems as if you can hookup a random DC supply, a BMS and a battery and magically all will work. But it is ...
Since it is a linear charger the input voltage should be higher than output voltage. By how much is shown by this graph in the datasheet.
So yes, you'll have to step up 5V, possibly to 9V at least. There would be greater power wastage if you step up to 12V.
Also as Tony mentioned in the comments, it'll be critical to have a Battery Management System (BMS) ...
No, a BMS is not a charger.
A BMS will not implement charging.
Connecting a battery with or without a BMS directly to a DC voltage is wrong.
Lithium cells need to be safely charged and that happens with a charger that implements CV-CC charging and will stop charging when batteries are determined to be fully charged.
There are many different BMS that all have different sets of features. Some BMS only provide information on state of charge. Other BMS might also do passive or active charge balancing of cells connected in series and also monitor state of health and temperature.
The charging process is not necessarily the main task of the BMS. Batteries could be charged with ...
You just modified a UL-listed charging block that interacts with AC power. That voided the UL listing, violated NEC 110.2 and 110.3, and made the charging block unsafe.
In AC, capacitors limit current. That capacitor was sized as a compromise between clean power and assuring that leakage current is not lethal in any likely failure mode of the ...
This is relatively common issue. Best addressed with chargers that actually have a protective ground (third terminal) that connects to the ground of the wall socket. Then shielding and metal parts (heat sink) inside of the PSU have a grounding path. If floating (as you tested with the capacitor removed) the secondary circuit may have too much common mode ...
Just a point, easiest way is to connect this panel directly to battery via 4.7 ohm power resistor (12v-6v)/1A=6ohm which will limits the current. A series diode is also necessary so energy does not flow from battery back to panel during night/cloud. The battery needs an overvoltage protection to cut the charging once reaches 7.2v.
All together can be really ...