Improve context server lifecycle management (#20622)

This optimizes and fixes bugs in our logic for maintaining a set of
running context servers, based on the combination of the user's
`context_servers` settings and their installed extensions.

Release Notes:

- N/A

---------

Co-authored-by: Marshall <marshall@zed.dev>
Co-authored-by: Marshall Bowers <elliott.codes@gmail.com>

crates/context_servers/src/context_servers.rs

@@ -8,7 +8,6 @@ use command_palette_hooks::CommandPaletteFilter;
 use gpui::{actions, AppContext};
 use settings::Settings;
 
-pub use crate::manager::ContextServer;
 use crate::manager::ContextServerSettings;
 pub use crate::registry::ContextServerFactoryRegistry;