This was the original argument for the King-Queen-Man-Women Word2Vec paper - it turns out no, not beyond basic categories. Yes to a degree. But all embeddings as trained based on what the creator decides they want them to do; to represent semantic(meanginful) similarity - similar word use - or topics or domains - or level of language use - or indeed to work multilingually and to clump together embeddings in one language, etc.

Different models will give you different results - many are based on search-retrieval, for which MTEB is a good benchmark. But those ones won't generally "excel" at what you propose, they'll just be in the same area.