What if it's a semi-auto like Formula 1 cars had back in the early 90s - the first generation flappy-paddles. None of the assists of today, just a button connected to a few solenoids at the gearbox, and perhaps a millisecond-long engine cut-out. They used to change gears in the blink of an eye, which is an age compared to the full electronic gearboxes they have now. They're probably very close to what MotoGP used before they went with seamless shift gearboxes only a few years ago, although MotoGP still uses a linkage between the gear lever the the actual gearbox.
The main philosophical difference, I guess, is whether the car has the ability to override your inputs (or lack of inputs) and do the gear changes by itself. Old F1 semi-autos had no override feature, but it wouldn't be too hard for someone to install, say, a Raspberry Pi in between the steering wheel buttons and the solenoids which did the actual shifting, and write some software which handles all of the gear changes. On the flipside, a conventional automatic gearbox with a small +/- lever tacked-on is definitely NOT doing any manual shifting, no matter how much it is trying to masquerade as one.
Probably the closest you can get, as a member of the general public, in terms of a device which blurs the lines between manual and auto, is a motorcycle with a quickshifter. It's essentially a proper manual 'box with a sensor that cuts engine power if the gear lever is moved. You can hold the throttle wide open and not use a clutch, simply change up by flicking your foot upwards. I mean, you can buy them and install them on virtually any motorcycle for a few hundred bucks.