Migrate to JETLS language server

I'd like to start a discussion about migrating from LanguageServer to JETLS. I think it's safe to say that JETLS will eventually replace the old one everywhere—so, this issue is more about "when" we're migrating rather than "if".

We have several open issues regarding LanguageServer and we still don't have an update mechanism for it. As @aviatesk commented here:

Since JETLS itself can be installed as the jetls executable Pkg app as long as you have the julia binary and network access, implementing automatic installation might actually be easier than it is for LanguageServer.jl (and as an additional benefit of JETLS, complete isolation of the server's dependency environment is already implemented).

This alone would solve most of our headaches.

JETLS is currently only compatible with Julia 1.12.2–1.12.x. We don't know how many people are using zed-julia on Julia 1.10 LTS but as folks had to upgrade to LanguageServer 5.0.0 manually, we could just document the migration path or leave old installations as they are.

@aviatesk, what shall we do with Julia 1.13.0-rc1 and the upcoming release?

I’d appreciate any feedback, or just a thumbs-up if you agree.

The issue names no files, tests, or entry points and is currently a migration discussion. First review the existing LanguageServer integration and JETLS compatibility across Julia versions, then establish an agreed migration path and acceptance criteria before implementation begins.