Is surface temperature relevant for the creation of high- and low pressures areas?
Your logic is wrong. Do not think of the atmosphere as a closed system. Your analogy of heating a bottle is not appropriate.
In uncomplicated terms, the Sun heats the ground, the ground radiates thermal energy heating the air just above the ground and the heated air rises. In rising, the air heated has less density than the surrounding air. By rising it exerts less pressure on the ground than the surrounding and thus has a lower pressure relative to the air surrounding it - it is a low pressure system.
The rising air reaches the tropopause, around 10 to 15 km above sea level, where it is no longer buoyant. Forced by the continually rising air it travels away from the heated zone. As it moves at such elevations  the air cools, increases in density and falls to the ground. As it falls the pressure it exerts on the ground is higher than the air surrounding it and it forms a high pressure system.
The system is best explained with Hadley Cells.
Air tends to rise around the equator and at latitudes 60° north and south, where most of the low pressure systems are located. Air tends to fall around latitude 30° north and south and the poles, where most of the high pressure systems are located.