I'm not a geologist, so don't take my incredulity for anything suggesting scientific fact, here.
One 'splainer I've seen[1] described the volcanic erruption as the result of seawater infiltrating a magma chamber or vent, flash-vaporising, and basically blowing straight up to a height of about 30km (roughly 100,000 ft). Think of this not simply as a pressure wave blasting upwards, but as a bolus of air (and steam / water vapour) punching up through the atmosphere. It's analogous to a water wave spiking up out of fluid --- after it rises up, it will collapse back down, then rebound up, repeating this several times.
The spike also both propogates out and creates a gravity-wave front which propagates outward, again creating a vertical wave across the top of the atmosphere.
We're used to gravity waves in water largely because water isn't compressible. Sound travels through water, but shock waves tend to have limited reach since water itself doesn't compress --- a water shock is rapidly transformed into a water gravity wave, with a surge and collapse. (How much energy is transmitted through either wave mode I don't know, though someone versed in fluid dynamics could probably say.)
Air is compressible, so a major part of the effect of an explosion is shock. That said, you can get gravity waves in air as well, and the Tonga erruption is apparently a demonstration of this.
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Notes:
1. Possibly GeologyHub on YT: https://yewtu.be/channel/UCYeGh5VML5XPr5jYnzh3J6g Though I've been viewing / reading many sources.
Update: found it here: https://yewtu.be/watch?v=YcCkQaLkfxA
But basically it has to do with buoyancy. A cloud or other layering of the atmosphere has a stable place in the vertical column. If the atmosphere passes over a mountain range that displaces the column vertically, the column returns to its normal position. In returning, the atmosphere overcorrects repeatedly and "bounces" back into position much like a single jump onto a mattress.
[1] https://en.wikipedia.org/wiki/Gravity_wave
[2] https://twitter.com/ggweather/status/1427061411604099077