feat(sessions): keep an idle session's prompt cache warm with a guarded keep-alive turn

Claude Code lets a subscription's one-hour prompt cache expire after an hour idle, and the first turn back re-writes the whole conversation at the cache-write rate; nearly every gap over an hour goes cold, while the saving is concentrated in gaps of one to four hours. Codeman now sends one short keep-alive turn five minutes before the expiry Claude Code reports on its statusline, so the next real prompt still reads the conversation from cache, and stops two hours (configurable) after the last real prompt.

Codeman owns the idle policy for these sessions, as agreed in Discussion #554: a launch with keep-warm on also carries idleCompaction: false in its one --settings JSON, so Claude Code's own idle compaction cannot replace the conversation with a summary a minute before the nudge. It is decided once per launch (keep-warm on, the statusLine exporter injected, Claude Code 2.1.290 or newer, an unknown version fails closed like --name), recorded on the mux record, and picked up by any relaunch; a launch with keep-warm off is byte-identical. A session switched on after launch is kept warm best-effort and the readout says so.

Every guard lives in one pure rulebook: the opt-in (an agent-spawned session does not inherit the app default), a launch that reports cache state, a warm 1h cache with enough tokens at stake and no compaction this gap, a live pane, no usage-limit pause, no respawn, Ralph, task or waiting agent, idle, no open dialog, an empty composer and no recent keystroke. The nudge is a submit and moves lastSubmitAt, which the response viewer's conversation correlation needs; the cap counts from its own persisted lastRealPromptAt instead. Read My Mind drops the exact nudge text, and the turn's stop hook and idle prompt open pre-acknowledged so nothing alerts. The last cache report and the clock survive a restart, so the timer re-arms.

src/mux-interface.ts

@@ -61,6 +61,11 @@ export interface MuxSession {
   ralphEnabled?: boolean;
   /** Whether the current launch carries the statusLine exporter; set on every create and respawn. */
   statusLine?: StatusLineExporter;
+  /**
+   * Whether the current launch carries `idleCompaction: false` in its `--settings` JSON (keep-warm
+   * on at launch, the exporter injected, Claude Code new enough); set on every create and respawn.
+   */
+  idleCompactionOff?: boolean;
   /**
    * This record was rebuilt from the tmux socket rather than from Codeman's own
    * bookkeeping, so everything on it but the name and the pid is a guess. Its
@@ -123,6 +128,10 @@ export interface CreateSessionOptions {
   effort?: EffortLevel;
   /** Claude advisor model, merged into the same `--settings` JSON (overridable via /advisor in-session) */
   advisorModel?: string;
+  /** The session's own prompt-cache keep-warm choice (undefined = app default); decides the `idleCompaction` opt-out. */
+  keepWarm?: boolean;
+  /** Spawned by another session: it does not inherit the keep-warm app default (`keepWarmOn`). */
+  spawnedByAgent?: boolean;
   /** tmux history-limit (scrollback lines) allocated when this session is created. */
   historyLimit?: number;
   /** Remote execution metadata for local tmux sessions wrapping SSH */
@@ -176,6 +185,10 @@ export interface RespawnPaneOptions {
   effort?: EffortLevel;
   /** Claude advisor model (preserved across respawns, merged into the same `--settings` JSON) */
   advisorModel?: string;
+  /** The session's own prompt-cache keep-warm choice, re-read at every relaunch (see CreateSessionOptions). */
+  keepWarm?: boolean;
+  /** Spawned by another session (see CreateSessionOptions). */
+  spawnedByAgent?: boolean;
   /** Original tmux history-limit retained for config parity; respawn cannot resize the existing pane. */
   historyLimit?: number;
   /** Remote execution metadata for local tmux sessions wrapping SSH */