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/extensions_ui/src/extensions_ui.rs

@@ -1,5 +1,4 @@
 mod components;
-mod extension_context_server;
 mod extension_registration_hooks;
 mod extension_suggest;
 mod extension_version_selector;