This is pretty much exactly what we've built at Sourcegraph. Microsoft had introduced (but pretty much abandoned before it even started) LSIF, a static index format for LSP servers which encodes in detail all possible LSP requests/responses, effectively.
We took that torch and carried it forward, building the spiritual successor called SCIP[0]. It's language agnostic, we have indexers for quite a few languages already, and we genuinely intend for it to be vendor neutral / a proper OSS project[1].