Since pioneered in the 1989 Ferrari this is usually done by computer now; the transmission forks and throttle are moved by an actuator, the whole thing is coordinated by a computer. The driver changes gear via paddles behind the steering wheel.
Here's Fernando Alonso having a go in a Supercar in 2022 at Albert Park, like he's never known anything else. I don't think he even blinks.
https://youtu.be/1f5QlfrODu8
There's a thing at Ferrari's site about it here: https://www.ferrari.com/en-EN/magazine/articles/great-ferrari-innovations-the-f1-semi-automatic-gearbox
Since around 2007 they pioneered 'seamless shifting' in F1, wherein - using some very trick arithmetic - two gears momentarily engage at the same time, so the next gear is 'queued' in milliseconds and the driveline simply keeps going with no interruption.