Such A-to-A adaptors and cables always have been prohibited by the USB spec, but people built them anyway. A common usecase for "illegal" A-A cables i remember was connecting PCIe cards (especially GPUs and mining cards) externally to riser sockets.
I bought a breadboard power supply and the options to feed it power are a barrel jack and usb-a. Considering the size of the thing mini or micro would have made way more sense.
The ones I have go trough the onboard voltage regulator and you can use them to power USB-devices. I suppose they've skipped diodes and other protective components so it can feed back to the circuit, but I haven't tested that.
An OTG setup needs all 5 pins of the micro-B connector. USB A cannot be used for OTG. If a USB-A port can act as a client, that's not OTG, it's a botched implementation.