Refactor app-server config loading into ConfigManager (#18442)

Localize app-server configuration loading in one place.

codex-rs/Cargo.lock

@@ -1508,11 +1508,13 @@ dependencies = [
  "sha2",
  "shlex",
  "tempfile",
+ "thiserror 2.0.18",
  "time",
  "tokio",
  "tokio-tungstenite",
  "tokio-util",
  "toml 0.9.11+spec-1.1.0",
+ "toml_edit 0.24.0+spec-1.1.0",
  "tracing",
  "tracing-opentelemetry",
  "tracing-subscriber",