Instinctively this feels like a two phase problem - start with some machine translation into a single spoken language and index that, then when people are querying do the same thing. When returning search results show them in the original language.

Why not create indexes for multiple languages, as that would also avoid double translation issues (e.g. GER [query] → ENG [index] → GER [document])?

Yes we've tried. It works. But jargon is hard. RAG with embeddings works all the same. The LLM doesn't mind receiving sources in Italian, french and German, and then outputting the answer in Japanese while providing the verbatim German jargon term in brackets