subagent: report turn liveness, and stop pre-checking continue

`status` could only answer running / starting / idle / killed / none,
because every turn ran against `&NoopSink` and the whole stream-json
stream was discarded. "Running" describes a wedged subagent exactly as
well as a busy one, leaving a caller to tell them apart from `ps` output
and CPU-time deltas.

So the daemon now keeps a `name -> last_event_at` clock, bumped by
`LivenessSink` on every line of every stream — stream-json events, plain
stdout chatter and stderr alike — and `status` reports its age on a
running answer: a few seconds means working, an age climbing into the
minutes with no end-of-turn todo means wedged. Nothing is read out of the
content; classifying *what* a subagent is doing is a separate question
and waits on its own driver work. In memory with the rest of this
daemon's state, dropped when the turn ends, no persistence.

The clock is seeded at the spawn rather than at the first line, so a
subagent that wedged before emitting anything still reports a climbing
age rather than no age at all — the case an age is worth most in.

Separately, `continue`'s existence pre-check is gone. It could only
repeat the lookup `Claude::spawn` was about to do, and its message —
"no session named `x` exists" — was false in the common failure: the
session existed, just not under the claude home + cwd `build_store`
resolved from. claude's own `--resume` is the authority and exits
non-zero (`does not match any session title`) rather than quietly
starting a fresh session, so the turn fails on its own. `classify_end`
appends the one fact the CLI's message lacks — the directory searched:

  claude error: no session matched the requested id or title (searched
  <claude_home> for cwd <cwd>; if the session was started elsewhere,
  pass `dir`)

The `dirs` map's durability is untouched; whether to persist it stays an
open operator decision.

Module doc, `docs/tools/subagent.md`, the `continue`/`status` tool
descriptions and the `base:claude-subagents` skill all updated — including
`continue`'s `dir` doc, which said "the daemon remembers it" without
saying that a restart is both when it forgets and when you most want it.

Refs #4330
Refs #4405

claude-plugins/plugins/base/skills/claude-subagents/SKILL.md

@@ -33,7 +33,10 @@ interrupt(name, force?)
 `start` and `continue` return as soon as the process is confirmed
 running, not once it finishes — a completion lands as a todo
 (`get_loose_ends`), same as any other producer. Use `status` for a
-zero-cost "is it still going" check; reach for `continue` only once you
+zero-cost "is it still going" check — for a running subagent it also
+reports how long since that turn last produced output, so a few seconds
+means it's working and an age climbing into the minutes means it's
+wedged and worth an `interrupt`. Reach for `continue` only once you
 actually have a new instruction for it, since that spends a turn.
 `interrupt` genuinely stops a running turn (`force: true` for SIGKILL).