Use rust-analyzer's flycheck as source of cargo diagnostics (#29779)

Follow-up of https://github.com/zed-industries/zed/pull/29706

Instead of doing `cargo check` manually, use rust-analyzer's flycheck:
at the cost of more sophisticated check command configuration, we keep
much less code in Zed, and get a proper progress report.

User-facing UI does not change except `diagnostics_fetch_command` and
`env` settings removed from the diagnostics settings.

Release Notes:

- N/A

crates/project/src/manifest_tree/server_tree.rs

@@ -247,20 +247,6 @@ impl LanguageServerTree {
         self.languages.adapter_for_name(name)
     }
 
-    pub fn server_id_for_name(&self, name: &LanguageServerName) -> Option<LanguageServerId> {
-        self.instances
-            .values()
-            .flat_map(|instance| instance.roots.values())
-            .flatten()
-            .find_map(|(server_name, (data, _))| {
-                if server_name == name {
-                    data.id.get().copied()
-                } else {
-                    None
-                }
-            })
-    }
-
     fn adapters_for_language(
         &self,
         settings_location: SettingsLocation,