fix(db,frontend): reserve DB connections for API and reduce frontend polling

Background tasks (ingestion, PDF resolution, scheduler) now acquire an
asyncio.Semaphore before checking out a DB connection, guaranteeing at
least N connections remain available for API request handlers. Removes
duplicate polling loop from PublicationsPage, debounces publication
reload on run-status changes, and increases poll interval from 5s to 15s
since SSE handles live discovery.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

app/db/background_session.py

@@ -0,0 +1,57 @@
+"""Semaphore-gated DB sessions for background tasks.
+
+Background tasks (ingestion, PDF resolution, scheduler) acquire a semaphore
+permit before checking out a database connection.  The semaphore cap is
+``pool_size + max_overflow - reserved_for_api``, which guarantees that at
+least *reserved_for_api* connections remain available for API request
+handlers at all times.
+"""
+
+from __future__ import annotations
+
+import asyncio
+import logging
+from collections.abc import AsyncIterator
+from contextlib import asynccontextmanager
+
+from sqlalchemy.ext.asyncio import AsyncSession
+
+from app.db.session import get_session_factory
+from app.logging_utils import structured_log
+from app.settings import settings
+
+logger = logging.getLogger(__name__)
+
+_semaphore: asyncio.Semaphore | None = None
+
+
+def _build_semaphore() -> asyncio.Semaphore:
+    pool_capacity = max(1, settings.database_pool_size) + max(0, settings.database_pool_max_overflow)
+    reserved = max(0, settings.database_reserved_api_connections)
+    limit = max(1, pool_capacity - reserved)
+    structured_log(
+        logger,
+        "info",
+        "db.background_semaphore_initialized",
+        pool_capacity=pool_capacity,
+        reserved_for_api=reserved,
+        background_limit=limit,
+    )
+    return asyncio.Semaphore(limit)
+
+
+def get_background_semaphore() -> asyncio.Semaphore:
+    global _semaphore
+    if _semaphore is None:
+        _semaphore = _build_semaphore()
+    return _semaphore
+
+
+@asynccontextmanager
+async def background_session() -> AsyncIterator[AsyncSession]:
+    """Yield a DB session after acquiring the background semaphore."""
+    semaphore = get_background_semaphore()
+    async with semaphore:
+        session_factory = get_session_factory()
+        async with session_factory() as session:
+            yield session