docs: record the late-injection render-hook fix + probe tool

Update the plan's status (validated against a real already-playing game),
add the "reactive-only hooking fails on late injection" lesson and the
self-deadlock ordering sub-lesson, and document tools/audio_probe in the
README. Mirrors commit c7be4ee.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

README.md

@@ -142,6 +142,17 @@ ctest --test-dir build -C Debug --output-on-failure
   shipping process-loopback capture (the fallback path) receives its audio by
   PID. Skips cleanly if the machine has no audio endpoint.
 
+### Debugging the render-hook against a real game
+
+[`tools/audio_probe`](tools/audio_probe) (`coop_audio_probe.exe <pid> [seconds]`)
+brings up the audio render-hook without Steam / RPT / the host UI: it creates the
+IPC block + audio ring the hook expects, injects `coop_hook.dll` into the target
+game, then drains the ring and prints per-stream format, captured-frame counts,
+peak amplitude (proves the audio is real, not silence), and overruns. It enables
+the hook's file trace (`%TEMP%\coop_hook.log`) for the run. Run it from
+`bin/<config>/`. **Kill the game between runs** — the loaded DLL locks
+`coop_hook.dll` against the next rebuild.
+
 ## Running the tool (manual, end-to-end)
 
 This needs Steam, a donor game that supports Remote Play Together, and a second