Using the LLM to mutate the user query is the way to go. A common practice for example to take the chat history of a chat, and rephrase a follow up question that might not have a lot of information density (e.g. follow up question is "and then what?" which is useless for search, but the LLM turns it into "after a contract cancellation, what steps have to be taken afterwards" or something similar, which provides a lot more meat to search with.

Using the LLM to mutate the input so it can be used better for search is a path that works very well (ignoring added latency and cost).