test: Campaign LA finish LA2 probe and idle gates

Prove idle play remains passive and live until cancellation, then converges through one truthful status teardown. Keep probe mode string-only so numeric enum aliases cannot expand the pinned v1 contract, and record the Windows/WSL gates.

src/AcDream.Headless/Configuration/HeadlessConfiguration.cs

@@ -167,9 +167,11 @@ internal sealed class HeadlessBotPolicyDescriptor
 /// The pinned launch-contract schema defines exactly two states for a
 /// session — ABSENT (mapped to <see langword="null"/>, meaning "play") or
 /// the literal string <c>"probe"</c> — so <see cref="Probe"/> is the only
-/// member; there is no explicit "play" spelling.
+/// member; there is no explicit "play" spelling. This deliberately uses
+/// <see cref="HeadlessConfigurationLoader"/>'s global camel-case,
+/// string-only enum converter; a per-enum converter with its default options
+/// would accidentally accept numeric <c>0</c> as a second probe spelling.
 /// </summary>
-[JsonConverter(typeof(JsonStringEnumConverter<HeadlessSessionMode>))]
 internal enum HeadlessSessionMode
 {
     Probe,