feat(P01): TASK-01-03 asyncpg pool lifespan + graceful degradation

Add @asynccontextmanager lifespan to the FastAPI app that creates an
asyncpg pool (min=1, max=10, command_timeout=10 — D-050) on app.state.pg_pool
and a PgStore on app.state.pg_store when PRAXIS_PG_DSN is set, applies
pg_migrations on startup, and closes the pool on shutdown.

Graceful degradation (REQ-NFR-MT-01): if PRAXIS_PG_DSN is unset, the
server starts with a WARNING and pg_pool/pg_store are None. The learner
voice loop (SQLite PraxisStore) is unaffected. Auth/operator routes will
return 503 (wired in SLICE-06).

---ci---
project: praxis
phase: 1
milestone: v0.4
status: execute
persona: backend-engineer
task: 01-03
requirements:
  covered: [REQ-MT-01, REQ-NFR-MT-01]
---/ci---

server/__main__.py

@@ -14,6 +14,7 @@ no audio/no tokens at runtime, not a crash.
 from __future__ import annotations
 
 import os
+from contextlib import asynccontextmanager
 from typing import Any
 
 from loguru import logger
@@ -32,6 +33,8 @@ from fastapi.middleware.cors import CORSMiddleware
 from fastapi.staticfiles import StaticFiles
 from pipecat.transports.smallwebrtc.connection import SmallWebRTCConnection
 
+from db.pg_migrate import apply_pg_migrations
+from db.pg_store import PgStore
 from db.store import PraxisStore
 from server.pipeline import build_pipeline
 from server.vc.verification import verify_credential
@@ -47,6 +50,54 @@ HOST = _env("PRAXIS_HOST", "0.0.0.0")
 PORT = int(_env("PRAXIS_PORT", "8789"))
 
 
+@asynccontextmanager
+async def lifespan(app: FastAPI):
+    """v0.4 — create the asyncpg Postgres pool on startup, close on shutdown.
+
+    Graceful degradation (D-050, REQ-NFR-MT-01): if PRAXIS_PG_DSN is unset,
+    the server starts without Postgres — the learner voice loop (SQLite)
+    is unaffected. app.state.pg_pool / app.state.pg_store are None in that
+    case and auth/operator routes return 503.
+    """
+    dsn = os.environ.get("PRAXIS_PG_DSN", "").strip()
+    if not dsn:
+        logger.warning(
+            "PRAXIS_PG_DSN not set — starting without Postgres (dev/no-pool mode). "
+            "Operator auth + cohort endpoints will be unavailable (503). "
+            "Learner voice loop (SQLite) is unaffected."
+        )
+        app.state.pg_pool = None
+        app.state.pg_store = None
+        try:
+            yield
+        finally:
+            return
+    import asyncpg
+
+    logger.info("Creating asyncpg Postgres pool (min=1, max=10, D-050)")
+    pool = await asyncpg.create_pool(
+        dsn=dsn,
+        min_size=1,
+        max_size=10,
+        command_timeout=10,
+    )
+    app.state.pg_pool = pool
+    app.state.pg_store = PgStore(pool)
+    try:
+        applied = await apply_pg_migrations(pool)
+        if applied:
+            logger.info(f"Postgres migrations applied: {applied}")
+        else:
+            logger.info("Postgres migrations up to date")
+        try:
+            yield
+        finally:
+            pass
+    finally:
+        await pool.close()
+        logger.info("Postgres pool closed")
+
+
 class WebRTCOffer(BaseModel):
     """Client→server WebRTC offer (SDP + type)."""
 
@@ -54,7 +105,7 @@ class WebRTCOffer(BaseModel):
     type: str = "offer"
 
 
-app = FastAPI(title="Praxis v0.1 voice server", version="0.1.0")
+app = FastAPI(title="Praxis v0.1 voice server", version="0.1.0", lifespan=lifespan)
 app.add_middleware(
     CORSMiddleware,
     allow_origins=["*"],  # dev — the client is a separate Vite origin