Do you know which version of Pump Express does the Xiaomi PLM13ZM supports? The Gemini and Cosmo uses (probably for cost reasons) the very oldest version, PumpExpress+ (basically, version 1). It can, at most, to the best of my knowledge, support 15W (9V x 1.67A or 12V x 1.25A, but the Gemini/Cosmo only uses 5V or 9V) which makes me think the PLM13ZM might (only) support a newer version of PumpExpress. Given the fairly large differences between generations, a charger supporting a newer PumpExpress version, isn't automatically backwards compatible (though it could be specifically designed to support multiple versions and/or multiple standards).
Your powerbank / cable combination only charging at ~0.5A seems a bit weird, as I have seen my own Cosmo draw close to 1.7A at 5V from a no-brand 2.4A 5V-only charger. I measured this using a Satechi USB-C power meter. It might be worth mentioning that only the left side USB port (on the same side as the headset jack) supports fast charging. The right side port (on the same side as the silvery button) only support regular charging, and only if the CoDi is enabled (though its screen doesn't have to be on) when connecting the cable. Even then, it might take up to a minute for the Cosmo to begin charging, so, unless you have special reasons (such as wanting to force a slow charge using the stock charger), I'd generally advice against using the right side port for charging.
As for forcing 9V into a a USB port that isn't in fast charging mode, well designed USB equipment should have a bit of overvoltage protection, though, most likely, nothing good would come out of it. All fast charging standards must start at 5V and unless the device sends a certain bit pattern (how this is done and what gets sent varies between fast charging standards and versions) to the charger, it'll stay at 5V. Just trying to force feed a port the wrong voltage, won't help.
As my USB cables seems to be branded by the (Swedish) reseller, I can't suggest any specific products, though any decent quality USB cable that physically fits, should support at least 2A (which is more than the Cosmo can draw anyway) at 5V, provided the charger or battery pack can provide that current. I'd generally advice against adapter tips for fast charging, as USB cables with older connector types might not be suitable for fast charging, unless they are specifically made to be used with (often included) adapter tips.