Welcome to the aftermarket. Even well known reputable companies have had problems with items that are "bolt on". Reminds me of the headaches I had to go through with installing a set of Crane 1.6 ratio roller rockers into the 3.1L V6 engine in my old 94 Z24. Crane said the rockers were straight bolt on/drop ins. Wrong. The lower intake manifold had to be machined/ground down in spots to provide clearance. The valve covers had to be modified to also provide clearance which meant removing the baffles that are part of the PCV system and then machining down the aluminum channels cast into the valve cover for air to be circulated through the PCV system. Finally, a metal baffle had to be welded over the opening for the PCV valve. All of this was for a "bolt on" part(s). I would be highly suspicious of any fitment claims from a no name brand overseas company.
With that said, the reason why the rapid flashing is happening as I explained above is because the turn signal circuit is expecting a higher electrical load/resistance that would be there in the stock setup. Looking at the pics for the aftermarket parts you have and because it's intended for the incandescent bulb setup in the older C-HR headlights, that pigtail with the gold box is probably a load resister added in to present the proper load to the turn signal circuit to mimic the stock incandescent bulb; since LEDs have a lower Ohm/resistance value than incandescent bulbs. My guess is further bolstered by the cooling fins on the exterior of that gold box. I don't know if the turn signal circuit will function properly in your car if it's presented with a higher than designed resistance. You'll have to give it a try. To do this as you're guessing, you'll have to splice in the appropriate factory connectors to the end of that pig tail to make it work. If you want to do it right, you'll need to use a volt ohm meter to measure the resistance of your factory LED turn signals. Then you need to do the same measurement of these aftermarket LED signals. I'm betting the aftermarket LEDs will come in with a smaller Ohm reading than the factory ones. You would then subtract the Ohm reading of the aftermarket signal from the factory signal. That difference number is the size load resister you need to wire as a bridge between the positive and negative wires for the turn signals.
If what I'm describing above is still not clear for you, I'd highly recommend you have a customization shop near you do the install work. Less aggravation and zero chance of screwing anything up.
Crystal clear, and I appreciate you taking the time to explain it. It just took me a second for it to click. The whole time I'm thinking these were "compatible" with my 2022, so I couldn't understand where I'd plug in a terminal (incandescent in this case) that I don't have. Now that I've worked it out, I think I can get these to work with the aforementioned hack.
It will all come down to load on the resistor as you say. I'm going to use their own supplied resistor, splicing my own LED connector which I already bought off Amazon. I actually bought both of the connectors I posted. Fairly inexpensive. And if that doesn't work, find a resistor that will.
I HATE blinky lights, it's sooooooo 60's. It's 2023 almost. My lights better be woke.
I'm many questionable things in life but defeatist is not one of them.
I shall report back. Hopefully I don't blow something up before that.
Cheers.