A limit to the airspace belonging to each country has to be defined.

Otherwise (for example) the Apollo missions would have violated USSR's airspace whenever the moon's orbit was above it's territory, which would make space unusable for everyone.

Well, technically if I'm not completely wrong the moon's ground track missed the southernmost extension of the USSR by a few degrees of latitude, but that nitpicking certainly does not put your point into question.

It would be a ridiculous definition of airspace if it included the vacuum of space.

So yes, Ballons are by definition in airspace because they use lighter than air buoyancy to rise and sattelites do not.

There's actually a non trivial amount of air in low earth orbit. For example the ISS or Starlink satellites would experienced drag and reenter in only a few years without periodic thrusting. At Starlink launch dispense they are even lower and reenter in days.

True, but I'd consider a height at which an object with sufficient speed will happily do a few orbits before eventually succumbing to drag to be safely in the "not air" realm.

I guess a balloon could drop bombs.

A balloon could also be in the way for airplanes. A balloon could also drop its payload, on purpose or by accident. The recent balloons have been reported to carry a load the size of up to several buses so I guess if that falls to ground it could cause quite some damage.

Not sure satellites can shoot missiles or drop bombs that could hit earth in any effective manner.

Low Earth satellites can indeed shoot missiles or drop bombs. It's what the DoD chief called for, https://breakingdefense.com/2018/08/space-based-missile-defe... and almost happens decades ago with Brilliant Pebbles.

It’s impossible to operate satellites if you need approval from every single country you might fly over.

Balloons can loiter over a location.

So can teenaged geosynchronous satellites.

Payloads from a balloon could be dropped, payloads released in orbit stay in orbit. LEO would be a very bad choice for anything intended to eventually interact with the ground in other ways than using electromagnetic waves.

Not a ground strike device. While it could of course be seen as a ground strike enabler, if the operator saw it as a sufficient counter to any opposing second strike capability, it's strictly an interceptor for suborbital passers-by.