I have one from a work piece of hardware which has a USB port that can operate in either device or host mode. 🥹

Those absolutely exist, but it's typically from older or more niche hardware.

I will note that you can't (usually) plug two computers into each other using a type a to a cable because USB still has a concept of strict host/client. USB-OTG allowed some portable client devices to operate in host mode with a special adapter - typically smartphones to use keyboards and such. I believe the Pi4's USB power port is one such port.

Type C more frequently has devices that can regularly operate in both modes, so you can do something like plug your iPhone into your android with an adapter for data transfer. So, if you have two computers and one can operate it's type a port in client mode, you could absolutely run USB A to A for computer to computer data transfer.

(I did all that from memory while kind of tired so corrections welcome)

Get an older external hard drive, live the dream.