As does molasses like when making refined sugar. Most unrefined sources of sugar naturally contain chemicals that act as stabilizers because it’s a side effect of many polysaccharides.
Note that even with the stabilising effect of straining and honey, real Greek yogurt (the stuff without additives) is never sold with admixtures. Once you mix stuff in you really are changing the consistency of the product and therefore its storage and transportation profile.
There's a scene in Silicon Valley [1] where Elrich Bachman is complaining that people keep taking his narrow spoons that he needs to mix in the jam in the little tub attached to his "Fa-Yeeh yogurt" (spelled "Fage". Surprisingly he pronounces it right! I'm Greek).
Bachman is talking about this product, Fage's split-cup Total yogurts:
https://gr.fage/total-2-split-cup
The reason there's a little tub and you have to tip it in and mix it up after you buy it is exactly because once you've disturbed the yogurt by mixing things in it, you don't have yogurt anymore but a gloopy goo with the consistency of thick cream and that just doesn't travel very well, especially if you want to be exporting your yogurt from Greece (where Fage has its plants) to the US (where Bachman complains about his spoons).
Also that gooey gloop is not what yogurt is supposed to be like. But I suppose that's just a matter of habit.
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People use honey and agave in salad dressings for their stabilizing effect by the way, so they’re also used as stabilizers if you want to be that obtuse about it.
People do use honey and agave as stabilizers in salad dressings, so obviously people consider them to be stabilizers </dumb semantic argument>
What?? I can't be the only one that gets plain greek yogurt and adds a tablespoon of honey or agave syrup and mixing it evenly before adding some granola + fruit. It's not that hard, and it's definitely not ultra-processed.