feat(heartbeat): add inactiveOnly mode (skip fire while workspace has active agents)

A new per-workspace heartbeat setting `inactiveOnly` (default true): when on, the
heartbeat SKIPS a scheduled fire whenever the configured workspace has any active
agents — a conversation whose persisted status is "active" (driving a turn) or
"queued" (waiting on the message queue). The fire is silently skipped (no run
recorded); the scheduler re-arms and retries at the next interval. Set false to
fire unconditionally (the prior behavior).

The check is wired against conversationStore.listConversations({ workspaceId,
status: ["active","queued"] }) at fire time — the orchestrator sets "active" on
turn start and "idle" on settle, so it is the live busy/idle signal. The spawned
heartbeat conversation lives in the dedicated heartbeat workspace, so a heartbeat
run never counts as an active agent of the configured workspace (no self-block).

- transport-contract: add inactiveOnly to HeartbeatConfig + UpdateHeartbeatRequest
- heartbeat config-store: default true, apply/persist, legacy-parse default true
- heartbeat service: injectable hasActiveAgents dep + skip logic in fire()
- heartbeat extension: wire hasActiveAgents against the conversation store
- transport-http: validate inactiveOnly (boolean) on PUT /workspaces/:id/heartbeat
- tests: config-store (+4), heartbeat service (+7), transport-http (+3)
- notes/heartbeat-setting-handoff.md: API contract for the frontend

Verification: typecheck EXIT 0; tests 2013 passed | 6 skipped; biome EXIT 0.

1 files changed, 13 insertions, 0 deletions

diff --git a/packages/heartbeat/src/extension.ts b/packages/heartbeat/src/extension.ts
index f245b7e..b044619 100644
--- a/packages/heartbeat/src/extension.ts
+++ b/packages/heartbeat/src/extension.ts
@@ -90,6 +90,19 @@ export const extension: Extension = {
       // Lazy (resolved at fire time, mirroring resolvePrompt).
       getWorkspaceCwd: async (wsId) =>
         (await conversationStore.getWorkspace(wsId))?.defaultCwd ?? null,
+      // inactiveOnly: the configured workspace is "busy" while any of its
+      // conversations are driving or queued for a turn. The orchestrator
+      // sets persisted status "active" on turn start and "idle" on settle,
+      // so a single store read (filtered to the configured workspaceId) is
+      // the live active-agent check. The heartbeat's own spawned conversation
+      // lives in the DEDICATED heartbeat workspace, so it never self-blocks.
+      hasActiveAgents: async (wsId) => {
+        const active = await conversationStore.listConversations({
+          workspaceId: wsId,
+          status: ["active", "queued"],
+        });
+        return active.length > 0;
+      },
     });
 
     // Reconcile stale runs + arm enabled workspaces on boot.