I think it's worth keeping in mind that word2vec was specifically trained on semantic similarity. Most embedding APIs don't really give a lick about the semantic space

And, worse, most latent spaces are decidedly non-linear. And so arithmetic loses a lot of its meaning. (IIRC word2vec mostly avoided nonlinearity except for the loss function). Yes, the distance metric sort-of survives, but addition/multiplication are meaningless.

(This is also the reason choosing your embedding model is a hard-to-reverse technical decision - you can't just transform existing embeddings into a different latent space. A change means "reembed all")