Use new language server info on remote servers (#35682)

* Straightens out the `*_ext.rs` workflow for clangd and rust-analyzer:
no need to asynchronously query for the language server, as we sync that
information already.
* Fixes inlay hints editor menu toggle not being shown in the remote
sessions

Release Notes:

- Fixed inlay hints editor menu toggle not being shown in the remote
sessions

crates/proto/src/proto.rs

@@ -121,8 +121,6 @@ messages!(
     (GetImplementationResponse, Background),
     (GetLlmToken, Background),
     (GetLlmTokenResponse, Background),
-    (LanguageServerIdForName, Background),
-    (LanguageServerIdForNameResponse, Background),
     (OpenUnstagedDiff, Foreground),
     (OpenUnstagedDiffResponse, Foreground),
     (OpenUncommittedDiff, Foreground),
@@ -431,7 +429,6 @@ request_messages!(
     (UpdateWorktree, Ack),
     (UpdateRepository, Ack),
     (RemoveRepository, Ack),
-    (LanguageServerIdForName, LanguageServerIdForNameResponse),
     (LspExtExpandMacro, LspExtExpandMacroResponse),
     (LspExtOpenDocs, LspExtOpenDocsResponse),
     (LspExtRunnables, LspExtRunnablesResponse),
@@ -588,7 +585,6 @@ entity_messages!(
     OpenServerSettings,
     GetPermalinkToLine,
     LanguageServerPromptRequest,
-    LanguageServerIdForName,
     GitGetBranches,
     UpdateGitBranch,
     ListToolchains,