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/Cargo.toml

@@ -17,7 +17,6 @@ test-support = []
 [dependencies]
 anyhow.workspace = true
 assistant_slash_command.workspace = true
-async-trait.workspace = true
 client.workspace = true
 collections.workspace = true
 context_servers.workspace = true
@@ -31,6 +30,7 @@ fuzzy.workspace = true
 gpui.workspace = true
 indexed_docs.workspace = true
 language.workspace = true
+log.workspace = true
 lsp.workspace = true
 num-format.workspace = true
 picker.workspace = true