I think your statement "adding to existing fulltext functionality" is subtly important: embeddings provide semantic search that complements traditional search algorithms.
Specifically, many applications are heavily dependent on names or other proper nouns, often without much context. You might refer to your dog by name without explanation, and a particular embedding might not pick that up. Proper names (people, places, street names) may have outsized importance for anchoring personalized or domain-specific search, but modest generic language models won't know about them.
Is there a specific way of dealing with this problem?