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/context_server/src/protocol.rs

@@ -16,7 +16,7 @@ pub struct ModelContextProtocol {
 }
 
 impl ModelContextProtocol {
-    pub fn new(inner: Client) -> Self {
+    pub(crate) fn new(inner: Client) -> Self {
         Self { inner }
     }