Is there only one way of measuring static air pressure? The age-old method of having a collapsable box with a certain volume and pressure? Or is there another way?

That "age old" barometer is the aneroid barometer, invented by Lucien Vidie in 1843.
Other barometers are the mercury barometer, invented by Evangelista Torricelli in 1644, and the contrabarometer, invented by Christian Huygens in 1670. A handfull of variants to these exist.
Two working priciples exist:
- Torricelli based: a liquid will be pushed up in a vacuum glass tube to a height depending on the air pressure. If the liquid is mercury, the avarage value at sea level is 76cm.
- Huygens based: an elastic medium will be more or less compressed depending on the air pressure. The elastic medium can be a spring, air, or anything a designer can imagine.
Maybe, within these we must also include the "digital" barometer, where the elastic medium is called a "sensor", such as a piëzo ceramic or quartz sensor. A chip takes care of the reading and the display.
There exists also the "stormglass" but this, I would not call a real barometer (no quantitative reading). Inventor is unknown, it is in use since about 1750. The principle is that specific crystals appear or disappear, sink or float in a oil/alcohol mixture with some additives - depending on the weather.