The confusion seems to arise from the fact that in your quote from Merriam Webster, you provided only the second of two adjectival definitions. The whole definition is:
Definition of vanilla
1 : flavored with vanilla
2 : lacking distinction : plain, ordinary, conventional
In the case of Yogurt, the first is in use. And in that context "plain" simply means "unflavored" (although anyone who has tasted plain yogurt will tell you, after they stop grimacing and smacking their lips, that it certainly does have a flavor!)
Outside of Yogurt, or food flavoring in general (and maybe the sub-field of botany dealing with Mexican orchids) "vanilla" is just a synonym for plain; i.e. lacking distinction, ordinary, or, to throw in another example of this kind of thing, "common or garden".
The reason "vanilla" took on that second meaning of plain/ordinary etc, is that in foods such as ice cream, yogurt, and custard, vanilla was by far the most commonly used flavoring, so much so that it came to be regarded as...well, plain, ordinary, and so on.
Other examples of this kind of thing are the aforementioned "common or garden", and "box, standard" (sometimes mispronounced as "bog standard")