feat(protocol): deliver Activity Lease model (Zero Background Workers)

Following a critical collaboration to resolve Windows terminal pop-ups, we've delivered a more robust 'Passive Activity' architecture:
- Terminology Pivot: Renamed 'Heartbeat' to 'Activity Lease' (Parking Permit model).
- Side-Effect Extension: tools/bb.ts now automatically extends the agent's lease whenever they perform real work (any CLI command).
- Passive Handshake: bb-init.mjs now only performs an initial registration/lease start, with no background loops.
- 100% Silence: Removed all background process spawning, ensuring zero terminal disruption on Windows.
- High Observability: Liveness is still tracked via the 15m threshold, but relies on activity rather than periodic pings.

OPERATIVE: silver-castle
SESSION: 2026-02-14-1330

tests/lib/agent-liveness.test.ts

@@ -6,7 +6,7 @@ import path from 'node:path';
 
 import {
   registerAgent,
-  heartbeatAgent,
+  extendActivityLease,
   deriveLiveness,
   agentFilePath,
 } from '../../src/lib/agent-registry';
@@ -29,7 +29,7 @@ async function withTempUserProfile(run: () => Promise<void>): Promise<void> {
   }
 }
 
-test('heartbeatAgent updates last_seen_at and increments version', async () => {
+test('extendActivityLease updates last_seen_at and increments version', async () => {
   await withTempUserProfile(async () => {
     const start = '2026-02-14T10:00:00.000Z';
     const next = '2026-02-14T10:05:00.000Z';
@@ -39,7 +39,7 @@ test('heartbeatAgent updates last_seen_at and increments version', async () => {
       { now: () => start }
     );
 
-    const result = await heartbeatAgent(
+    const result = await extendActivityLease(
       { agent: 'active-agent' },
       { now: () => next }
     );