Add richer LSP server example (#20017)

[shashi1687]

What this PR does

This adds a new “head-start” LSP server example under:
crates/rust-analyzer/examples/rust_analyzer_lsp_example/
It demonstrates how to:

• Capture document edits with textDocument/didChange and log the URI
• Stub out textDocument/completion (returns an empty list)
• Stub out textDocument/formatting (returns no edits)

What the example does

1. Initialization
   • Opens JSON-RPC over stdio
   • Advertises full text sync, a completion provider, and a formatting provider
2. Main loop
   • Logs every buffer change (didChange)
   • Replies to completion requests with {"isIncomplete":false,"items":[]}
   • Replies to formatting requests with []
   • Handles clean shutdown on shutdown/exit

This gives anyone embedding rust-analyzer a minimal “plug-in” template for completions and formatting.

About the author’s note

“The current LSP example is a good, minimal demonstration. It shows how to respond to textDocument/definition. I used it to make an example that includes capturing content from textDocument/didChange and using it to provide textDocument/completion and textDocument/formatting functionality…”

• We’ve taken that idea and upstreamed it as a fresh, in-tree example.
• No external code was copied verbatim—just a clean re-implementation.

Testing & Validation

1. Build

   cargo build -p rust-analyzer --example rust_analyzer_lsp_example

[ShoyuVanilla]

I think this example should be located under lib/lsp-server/examples/ like the previous one

[ShoyuVanilla]

Well, I think that the original intention of the OP in #20017 is asking opinions about adding their existing lsp-server example codes to rust-analyzer repository, not implementing new examples, though I don't have strong opinion on it.

What the example does

...
This gives anyone embedding rust-analyzer a minimal “plug-in” template for completions and formatting.

Besides that, I think this example is not that "richer" than existing goto_def.rs one because most of the scaffolding codes are almost same, and I can't really understand what is the intention of the message handling examples in this PR: It's just a personal thought but I think it would be better to be somewhat more exhaustive on different kinds of messages or more focused or detailed on a specific category of messages.
In short, I'd like to ask "What would be the proper filename for this when located in the same directory with goto_def.rs example?"

[lnicola]

Yeah, I think a single example would be better.