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/extension_host/src/extension_host.rs

@@ -1130,6 +1130,10 @@ impl ExtensionStore {
                         .remove_language_server(&language, language_server_name);
                 }
             }
+
+            for (server_id, _) in extension.manifest.context_servers.iter() {
+                self.proxy.unregister_context_server(server_id.clone(), cx);
+            }
         }
 
         self.wasm_extensions