This was in Sport mode, so it shifts automatically. I'm holding a phone and recording with one hand and steering wheel with the other (not the safest thing, I know 😅) it would be impossible to shift also.. But I know what you mean, it has a significant lag when shifting manually, I was hitting the limiter like crazy for the first couple of days when i just bought the car.
Buy one that's well serviced and maintained, don't hesitate to give bit more money for a good example. They are old and pretty complicated machines so you want one that's been cared for. But for a first car I would suggest you to get a 1st gen Impreza with a manual gearbox and low/high gear range if you can get them where you live. Old Imprezas are awesome, you don't even have to buy a turbo, 1.8 will be more than enough to experience a proper Subaru.
Move shifter in a manual position and it should be in Sport as long as you don't touch it and shift gears manually. There's a light on the dashboard that tells you when you're in Sport.