context_store: Refactor state management (#29910)

Because we instantiated `ContextServerManager` both in `agent` and
`assistant-context-editor`, and these two entities track the running MCP
servers separately, we were effectively running every MCP server twice.

This PR moves the `ContextServerManager` into the project crate (now
called `ContextServerStore`). The store can be accessed via a project
instance. This ensures that we only instantiate one `ContextServerStore`
per project.

Also, this PR adds a bunch of tests to ensure that the
`ContextServerStore` behaves correctly (Previously there were none).

Closes #28714
Closes #29530

Release Notes:

- N/A

crates/collab/src/tests/integration_tests.rs

@@ -6709,8 +6709,6 @@ async fn test_context_collaboration_with_reconnect(
         assert_eq!(project.collaborators().len(), 1);
     });
 
-    cx_a.update(context_server::init);
-    cx_b.update(context_server::init);
     let prompt_builder = Arc::new(PromptBuilder::new(None).unwrap());
     let context_store_a = cx_a
         .update(|cx| {

crates/collab/src/tests/test_server.rs

@@ -709,6 +709,7 @@ impl TestClient {
         worktree
             .read_with(cx, |tree, _| tree.as_local().unwrap().scan_complete())
             .await;
+        cx.run_until_parked();
         (project, worktree.read_with(cx, |tree, _| tree.id()))
     }