Why do drugs that increase GABA activity have an anxiolytic effect

What is the neuroscience of this? Benzos, barbituates as well at OTC supplements like theanine or taurine work because of the effect they have on GABA system.

So what is the neuroscience of why increasing GABA activity will stop or reduce anxiety? What brain areas are involved?

I know GABA causes Cl- ions to enter the cell, making the neurons less excitable (is that the scientific word, excitable)? But how does this translate into anxiolytic effects?

Does anxiety result from overactivity in certain brain areas, and GABA drugs bring that back down to baseline, or is anxiety something that happens with regular brain activity and GABA brings neuron activity to below baseline? One would be like if you had a fast heart rate and you used a drug to bring it back to normal, vs having a normal heart rate and taking a drug to bring it to below normal as a metaphor.

Is anxiety from overactivity in certain brain areas, or will regular brain activity cause it?
Which brain areas are involved? I assume the amygdala, but am not sure what else.
Are there brain areas involved in anxiety that do not have GABA receptors?