docs: add rs-exec browser lifecycle diagnostic note to AGENTS.md

Browser state now persists across exec:browser calls within a session (rs-exec@20833eb).
If regression occurs, check rs-exec deleteTask to confirm it is not killing Chrome.

Author: lanmower

AGENTS.md

@@ -21,3 +21,7 @@ This file collects facts that are **not derivable by reading the code** and woul
 ## CI / Deploy
 
 - **Declaudeify workflow force-rewrites history on every push.** After `git push`, a GitHub Action strips "Claude" strings from commit messages and force-pushes. Local `main` always diverges from origin after CI runs. Run `git pull --rebase` before every second push in a session, or the second push is rejected.
+
+## Browser Automation (exec:browser / rs-exec)
+
+- **Browser lifecycle is owned by Claude session, not task.** rs-exec's `deleteTask` (called after every `exec:browser` invocation by rs-plugkit) previously killed Chrome on every call. Fixed in rs-exec@20833eb (April 2026): deleteTask is now pure task-cleanup; the managed browser persists for the entire Claude session and only tears down once at session end via `session_end.rs::run`. **Impact**: Browser state (page, localStorage, cookies, JS context) now survives across consecutive `exec:browser` calls within a session. **Regression test**: If page resets every command, check `C:/dev/rs-exec/src/rpc.rs:75` — if deleteTask is calling `kill_session_browser(sid)` again, that's the bug.