Sorry for the half reply (I cannot check it physically right now): if you search for "BT keyboard with slot" in the images section of a search engine (DDG), a few similar to mine will come out: I have the one with the mousepad in the bottom-right corner. I believe that the manufacturers distribute the product for different brands (so, for example, I see "Hot-sale-keyboard-bluetooth-touchpad" on Alibaba, or a "Texet Bluetooth Keyboard Touchpad BTK SLOT").

BTW: battery life is never a problem. The rare events in which I find myself with the red light blinking, I just hook up a portable power bank.

Not the poster, but this is the one I got, works well, though it definitely can't compare to a mechanical keyboard: https://www.amazon.com/gp/product/B00MUTWLW4 Logitech K480 bluetooth.

Unfortunately I can't recommend boox anymore, a tiny crack appeared on my note air pretty much where my thumb goes when holding it and spread across the entire display; warranty was useless of course.