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>

Cargo.lock

@@ -2572,6 +2572,7 @@ dependencies = [
  "clock",
  "collab_ui",
  "collections",
+ "context_servers",
  "ctor",
  "dashmap 6.0.1",
  "derive_more",
@@ -2818,7 +2819,6 @@ name = "context_servers"
 version = "0.1.0"
 dependencies = [
  "anyhow",
- "async-trait",
  "collections",
  "command_palette_hooks",
  "futures 0.3.30",
@@ -4205,7 +4205,6 @@ dependencies = [
  "assistant_slash_command",
  "async-compression",
  "async-tar",
- "async-trait",
  "client",
  "collections",
  "context_servers",
@@ -4222,6 +4221,7 @@ dependencies = [
  "http_client",
  "indexed_docs",
  "language",
+ "log",
  "lsp",
  "node_runtime",
  "num-format",