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It is.

rather it's even smaller, it simply has the inner part of a usb c connector - exactly the thickness of the pcb

In the implementation, the design uses a 'card edge' type connector with the whole PCB fitting into the constraint of the thickness of the center blade of the USB-C connector. So when charging, the board slots into the cable-end connector, and when not charging there is only the PCB. The PCB has cut-outs for the cable-end connector to fit into the PCB -- so like you're saying, but even thinner.

Thought the same but from what I can see those are somewhat uncommon, presumably you are unable to affix them to the board as securely as the typical connectors

The images in the GitHub show that the card has this.