refactor: align backend layout and supabase infra

Consolidate backend modules/tests under the backend package while syncing Supabase compose/env config and related plans.

backend/src/core/db/base.py

@@ -0,0 +1,37 @@
+from __future__ import annotations
+
+from datetime import datetime
+
+from sqlalchemy import DateTime, func
+from sqlalchemy.orm import DeclarativeBase, Mapped, mapped_column
+
+
+class Base(DeclarativeBase):
+    """Base class for all ORM models."""
+
+    pass
+
+
+class TimestampMixin:
+    """Adds created_at and updated_at timestamps."""
+
+    created_at: Mapped[datetime] = mapped_column(
+        DateTime(timezone=True),
+        server_default=func.now(),
+        nullable=False,
+    )
+    updated_at: Mapped[datetime] = mapped_column(
+        DateTime(timezone=True),
+        server_default=func.now(),
+        onupdate=func.now(),
+        nullable=False,
+    )
+
+
+class SoftDeleteMixin:
+    """Adds soft delete timestamp column."""
+
+    deleted_at: Mapped[datetime | None] = mapped_column(
+        DateTime(timezone=True),
+        nullable=True,
+    )