My super basic faucet handles are exactly that…you twist it left-right to set temp and tilt it up-down for pressure from off to full. We just leave it rotated wherever we like it for temp and tilt up to turn on each time to the desired pressure. Our water pressure is always variable, so the amount tilted up varies, but the “rotational temp” almost never needs changing. There’s no fancy thermostatic valve in these like some shower have. There’s even those fancy kitchen sink faucets that remember everything and you just tap them with your hand and they automatically turn on/off to your settings of temp and pressure. I think they are called “touchless faucets”. Pretty sure even Ikea sells one.

I feel like sink handles like mine are super common, too. I’ve had similar ones in the states and in Europe…