Well, you've fooled yourself into thinking you understand something when you don't. I say this as someone with a PhD in the topic, who has taught many students, and published dozens of papers in the space.

The operation of adding BoW vectors together has nothing to do with the operation of adding together word embeddings. Well, aside from both nominally being addition.

It's like saying you understand what's happening because you can add velocity vectors and then you go on to add the binary vectors that represent two binary programs and expect the result to give you a program with the average behavior of both. Obviously that doesn't happen, you get a nonsense binary.

They may both be arrays of numbers but mathematically there's no relationship between the two. Thinking that there's a relationship between them leads to countless nonsense conclusions: the idea that you can keep adding word embeddings to create document embeddings like you keep adding BoWs, the notion that average BoWs mean the same thing as average word embeddings, the notion that normalizing BoWs is the same as normalizing word embeddings and will lead to the same kind of search results, etc. The errors you get with BoWs are totally different from the errors you get with word or sentence or document embeddings. And how you fix those errors is totally different.

No. Nothing at all makes sense about word embeddings from the point of BoW.

Also, yes BoW is a total dead end. They have been completely supplanted. There's never any case where someone should use them.