refactor: Extract shared MCP Stdio NDJSON parsing loop into mcp-stdio library

Cargo.lock

@@ -1375,6 +1375,7 @@ dependencies = [
  "clap",
  "dirs 7.0.0",
  "futures-util",
+ "mcp-stdio",
  "reqwest",
  "serde_json",
  "tokio",
@@ -1404,6 +1405,14 @@ dependencies = [
  "tracing-subscriber",
 ]
 
+[[package]]
+name = "mcp-stdio"
+version = "0.1.0"
+dependencies = [
+ "tokio",
+ "tracing",
+]
+
 [[package]]
 name = "measure_time"
 version = "0.9.0"
@@ -1527,6 +1536,7 @@ name = "nvim-core"
 version = "0.1.0"
 dependencies = [
  "dirs 7.0.0",
+ "mcp-stdio",
  "rmcp",
  "rmp-serde",
  "rmpv",