Ensure context servers are spawned in the workspace directory (#35271)

This fixes an issue where we were not setting the context server working
directory at all.

Release Notes:

- Context servers will now be spawned in the currently active project
root.

---------

Co-authored-by: Danilo Leal <danilo@zed.dev>

crates/project/src/project.rs

@@ -998,8 +998,9 @@ impl Project {
             cx.subscribe(&worktree_store, Self::on_worktree_store_event)
                 .detach();
 
+            let weak_self = cx.weak_entity();
             let context_server_store =
-                cx.new(|cx| ContextServerStore::new(worktree_store.clone(), cx));
+                cx.new(|cx| ContextServerStore::new(worktree_store.clone(), weak_self, cx));
 
             let environment = cx.new(|_| ProjectEnvironment::new(env));
             let manifest_tree = ManifestTree::new(worktree_store.clone(), cx);
@@ -1167,8 +1168,9 @@ impl Project {
             cx.subscribe(&worktree_store, Self::on_worktree_store_event)
                 .detach();
 
+            let weak_self = cx.weak_entity();
             let context_server_store =
-                cx.new(|cx| ContextServerStore::new(worktree_store.clone(), cx));
+                cx.new(|cx| ContextServerStore::new(worktree_store.clone(), weak_self, cx));
 
             let buffer_store = cx.new(|cx| {
                 BufferStore::remote(
@@ -1428,8 +1430,6 @@ impl Project {
         let image_store = cx.new(|cx| {
             ImageStore::remote(worktree_store.clone(), client.clone().into(), remote_id, cx)
         })?;
-        let context_server_store =
-            cx.new(|cx| ContextServerStore::new(worktree_store.clone(), cx))?;
 
         let environment = cx.new(|_| ProjectEnvironment::new(None))?;
 
@@ -1496,6 +1496,10 @@ impl Project {
 
             let snippets = SnippetProvider::new(fs.clone(), BTreeSet::from_iter([]), cx);
 
+            let weak_self = cx.weak_entity();
+            let context_server_store =
+                cx.new(|cx| ContextServerStore::new(worktree_store.clone(), weak_self, cx));
+
             let mut worktrees = Vec::new();
             for worktree in response.payload.worktrees {
                 let worktree =