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/session-submit-verifier.ts

@@ -65,6 +65,28 @@ export function promptStillInComposer(screen: string, prompt: string, glyph: str
   return head.length > 0 && composer.startsWith(head);
 }
 
+/**
+ * Whether the composer holds nothing: the LAST `glyph` line after the glyph, and every
+ * continuation line below it down to the composer's bottom rule (a draft that opens with a
+ * newline leaves the glyph line itself blank). Undefined when there is no composer line or no
+ * rule under it to bound the read (a shell, a dialog, a direct-PTY session): nothing can be
+ * said. The prompt-cache keep-warm refuses to type unless this is true: `send-keys -l` would
+ * append its nudge to whatever draft sits there, and the Enter would submit both.
+ */
+export function composerIsEmpty(screen: string, glyph: string): boolean | undefined {
+  if (!glyph) return undefined;
+  // The structure is read at column 0, before any trimming: Claude Code draws the glyph line and
+  // both rules there and indents every continuation line, so a draft line that holds the glyph or
+  // starts with a rule (`  ❯`, `  ───`) can never pass for the composer's own edges.
+  const lines = stripAnsi(screen).split('\n');
+  let at = lines.length - 1;
+  while (at >= 0 && !lines[at].startsWith(glyph)) at--;
+  if (at < 0) return undefined;
+  const end = lines.findIndex((l, i) => i > at && l.startsWith('\u2500'));
+  if (end < 0) return undefined;
+  return compact(lines[at].slice(glyph.length) + lines.slice(at + 1, end).join('')).length === 0;
+}
+
 export interface SubmitVerifierDeps {
   /** The rendered pane, or null when there is none to read. */
   capture: () => string | null | undefined;