Those cables are cheap that it’s maybe worth a try, IMHO.
If I remember it correctly the only thing any USB-A to USB-C adaptor has to have to properly allow backwards compatibility is 2 resistors, which are stupidly cheap components (yeah, it will never be able to support things like USB PD charging - which can do all the way up to 100W - but it should still handle about 4.5W from a USB Host device and up to 15W from a dumb charger, which should be more than enough for a wireless keyboard).
Have you tried another USB-A to USB-C cable?
Those cables are cheap that it’s maybe worth a try, IMHO.
If I remember it correctly the only thing any USB-A to USB-C adaptor has to have to properly allow backwards compatibility is 2 resistors, which are stupidly cheap components (yeah, it will never be able to support things like USB PD charging - which can do all the way up to 100W - but it should still handle about 4.5W from a USB Host device and up to 15W from a dumb charger, which should be more than enough for a wireless keyboard).