So far ( I don’t have many) all of my USB rechargeable cells would not charge USB C to USB C. But A to C works. So your situation is what I would call normal.
If my cable can charge my phone with the larger battery, I don’t think the wall charger/power block is the issue. It could of been design this way for a reason. Probably a slower charge.
Venom, i have charger with type a and type c in. It can charge one samsung phone with type-c to type-c cable and can’t charge another newer one. But on another charger same cable same phone work well. At least topic starter can try, maybe it will work with another charger.
The fact that Lumintop 14500s won’t charge with C-to-C is not correct, but it is normal. I’ve found this is the case with Acebeam 920mAh batteries as well.
It's common for "cheap" flashlight, to not support the PD standard, and not have the two resistors on the USB C connectors, telling the other USB C device, that they want power.
So they Just don't work with USB C to USB C.
Almost all My USB C flashlight, only work with USB A - USB C cables.
I don’t have any suggestions based on experience. The ones I have are all USB 2.0, and therefore have only 5 conductors in them (through there may be more than one VBUS or GND conductor in there; I’ve never cut them open). I only have one that is rated for 100W and I hate it; it holds every bend that was in it when it came out of the package, and its outer sheath is kind of sticky.
If you are just looking for power rather than high speed data, the Anker Powerline cables look nice, especially the Powerline III, but they are USB 2.0.
I’ve been meaning to get at least one USB 3.1 C-to-C cable just for experiments, but I expect they will be thick and stiff because they have at least 9 conductors. I’m wondering if I should jump straight to USB 3.2, but that will be even thicker with 20+ conductors.
I didn’t even seem the ones you link to on Amazon.
I found this in the Q&A on Amazon about the Lumintop 14500. Copy & paste
“It will light up red when charging and green when it is fully charged. And I would also like to note when I plug into certain USB C fast charging cords it will not work with the battery. It seems to only work slower/ cheaper USB C charging cords to charge properly.”