USB On-The-Go

USB-C has obfuscated things but I was hoping the following would work:

Buy a Y-cable from Ali Express that has USB-C male to plug into the phone, and both USB-C female and USB-A female sockets. Plug keyboard into the USB-A and the charger into USB-C.

But it doesn't work, and I suspect it's a software limitation at least on my phone (Moto G Play 2023). If the charger is plugged in first, the phone will charge but not use the keyboard. If the keyboard is plugged in first, the phone will use it, but not charge. I think the wires are there to make it all work, but the phone's OS just doesn't support this scenario. Pity.

Needless to say documentation is nonexistent so I don't actually know what's in the cable. For all I know, the two female sockets are just connected in parallel.

USB-C never defined a Y cable and so they never figured out how that would work. If such a cable works anywhere it is either luck, or there is some chip inside that checks for power messages from either end but otherwise looks like a straight through cable. Even then it will be tricky because if the two devices want different voltages from the charger only one can get their way.

I can't blame the USB-C people for not working on this case. It is a lot harder than it seems to make work, and of limited use. Just get a USB-C hub if you need this ability.

Isn't this exactly what USB-C docks are for?

I've seen plenty of those devices, where you have a female USB-C socket to connect a charger to, a range of other female USB-C, USB-A and other ports for peripherals and a short cable with a male USB-C plug to connect to a laptop. If everything works, the dock will act as a power source for both the peripherals and the laptop, but will act like a hub on the data lines, with the laptop being the host.

I wonder if it would work just the same if you connected a phone instead of a laptop to the "host" cable.

That is what a dock is for. OP wants a simple and cheap cable instead which isn't really possible in the generic sense (though it might work in some limited way)

I've connected my phone to the host cable of a dock before and everything worked. (I didn't try the HDMI output, but sound on the dock just worked)