There are many excellent search APIs to start your integration: symbolic (Elasticsearch, Solr, Algolia), semantic (Weaviate, Pinecone, Milvus, Vespa). But in all projects, there is some heavy lifting: create and setup indices, cleanse and send data, generate queries, display results… This is where plugins like WPSOLR are really useful, they manage for you the submerged part of the iceberg.
Cohere embeddings were indeed considered, on average, more accurate than OpenAI embeddings by a WooCommerce client
But of course, it entirely depends on the data. No solution is absolute. This is why it is so important to be able to compare