refactor: rename the application package to docsgpt

The backend import package is now docsgpt, the name it will carry on PyPI;
application was far too generic to install into anyone's site-packages.
git mv plus a mechanical rewrite of every import, dotted string and path
reference: 734 Python files, the compose files, Dockerfile, workflows, docs,
setup scripts, devcontainer, k8s manifests, vscode config, pytest and coverage
config, .gitignore. Behaviour is unchanged.

Kept for one release:
- A top-level application package whose meta-path finder resolves
  application.x.y to the already-imported docsgpt.x.y object, so old imports
  and entry points (celery -A application.app.celery,
  uvicorn application.asgi:asgi_app) keep working with a FutureWarning.
- Celery registers every application.* task name as an alias of its
  docsgpt.* task on start-up, so messages queued by the previous release still
  run. The redbeat key prefix moves to redbeat:docsgpt:v2: so schedule entries
  the previous release wrote are left unread instead of firing twice.

The backend image builds from the repository root (docker build -f
docsgpt/Dockerfile .) so it can ship the alias package; a root .dockerignore
allow-lists docsgpt/ and application/ and keeps caches, local data, .env
files, the sample index files and the Dockerfile out. Compose and the image
workflows point at the new context.

docsgpt/storage/db/engine.py

@@ -0,0 +1,98 @@
+"""SQLAlchemy Core engine factory for the user-data Postgres database.
+
+The engine is lazily constructed on first use and cached as a module-level
+singleton. Repositories and the Alembic env module both obtain connections
+through this factory, so pool tuning lives in one place.
+
+``POSTGRES_URI`` can be written in any of the common Postgres URI forms::
+
+    postgres://user:pass@host:5432/docsgpt
+    postgresql://user:pass@host:5432/docsgpt
+
+Both are accepted and normalized internally to the psycopg3 dialect
+(``postgresql+psycopg://``) by ``docsgpt.core.settings``. Operators
+don't need to know about SQLAlchemy dialect prefixes.
+"""
+
+from typing import Optional
+
+from sqlalchemy import Engine, create_engine, event
+
+from docsgpt.core.settings import settings
+
+_engine: Optional[Engine] = None
+
+
+def _resolve_uri() -> str:
+    """Return the Postgres URI for user-data tables.
+
+    Raises:
+        RuntimeError: If ``settings.POSTGRES_URI`` is unset. Callers that
+            reach this path without a configured URI have a setup bug — the
+            error message points them at the right setting.
+    """
+    if not settings.POSTGRES_URI:
+        raise RuntimeError(
+            "POSTGRES_URI is not configured. Set it in your .env to a "
+            "psycopg3 URI such as "
+            "'postgresql+psycopg://user:pass@host:5432/docsgpt'."
+        )
+    return settings.POSTGRES_URI
+
+
+#: Per-statement wall-clock cap applied to every connection handed out by
+#: the engine. 30s is generous for interactive hot paths (reads under a few
+#: hundred ms are normal) but still catches a runaway query before it
+#: stacks up on PgBouncer or holds locks indefinitely.
+STATEMENT_TIMEOUT_MS = 30_000
+
+
+def get_engine() -> Engine:
+    """Return the process-wide SQLAlchemy Engine, creating it if needed.
+
+    The engine applies a server-side ``statement_timeout`` to every
+    connection it hands out via a ``connect`` event, so both
+    :func:`db_session` and :func:`db_readonly` inherit the same
+    guardrail.
+
+    Returns:
+        A SQLAlchemy ``Engine`` configured with a pooled connection to
+        Postgres via psycopg3.
+    """
+    global _engine
+    if _engine is None:
+        _engine = create_engine(
+            _resolve_uri(),
+            pool_size=10,
+            max_overflow=20,
+            pool_pre_ping=True,     # survive PgBouncer / idle-disconnect recycles
+            pool_recycle=1800,
+            future=True,
+        )
+
+        @event.listens_for(_engine, "connect")
+        def _apply_session_guardrails(dbapi_conn, _record):
+            # Apply as a SQL ``SET`` (not a libpq ``options=-c ...``
+            # startup parameter) so the engine works behind
+            # PgBouncer-style poolers — notably Neon's ``-pooler``
+            # endpoint, which rejects startup options. Explicit
+            # ``commit()`` so the session-level SET survives SA's
+            # transaction resets on pool return.
+            with dbapi_conn.cursor() as cur:
+                cur.execute(f"SET statement_timeout = {STATEMENT_TIMEOUT_MS}")
+            dbapi_conn.commit()
+
+    return _engine
+
+
+def dispose_engine() -> None:
+    """Dispose the pooled connections and reset the singleton.
+
+    Called from the Celery ``worker_process_init`` signal so each forked
+    worker gets a fresh pool instead of sharing file descriptors with the
+    parent process (which corrupts the pool on fork).
+    """
+    global _engine
+    if _engine is not None:
+        _engine.dispose()
+        _engine = None