language servers: Fix wrong language server name (#20428)

This fixes the issue of multiple language servers showing up as `node`
in the language server logs dropdown.

It does this by changing `language_server.name()` to return the
adapter's name, not the binary name, and changing types to make sure
that we always use this.

Release Notes:

- Fixed language server names showing up only as `"node"`

---------

Co-authored-by: Sam Rose <hello@samwho.dev>
Co-authored-by: Bennet <bennet@zed.dev>

crates/collab/src/tests/integration_tests.rs

@@ -5130,11 +5130,10 @@ async fn test_lsp_hover(
         });
         let new_server_name = new_server.server.name();
         assert!(
-            !servers_with_hover_requests.contains_key(new_server_name),
+            !servers_with_hover_requests.contains_key(&new_server_name),
             "Unexpected: initialized server with the same name twice. Name: `{new_server_name}`"
         );
-        let new_server_name = new_server_name.to_string();
-        match new_server_name.as_str() {
+        match new_server_name.as_ref() {
             "CrabLang-ls" => {
                 servers_with_hover_requests.insert(
                     new_server_name.clone(),