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/models/__init__.py

@@ -0,0 +1,5 @@
+from __future__ import annotations
+
+from models.profile import Profile
+
+__all__ = ["Profile"]

backend/src/models/profile.py

@@ -0,0 +1,43 @@
+from __future__ import annotations
+
+import uuid
+
+from sqlalchemy import String, Text
+from sqlalchemy.dialects.postgresql import UUID
+from sqlalchemy.orm import Mapped, mapped_column
+
+from core.db.base import Base, SoftDeleteMixin, TimestampMixin
+
+
+class Profile(TimestampMixin, SoftDeleteMixin, Base):
+    """User profile model.
+
+    Note: The `id` column references auth.users(id) in Supabase.
+    This is a business table managed by SQLAlchemy, with the foreign key
+    relationship to Supabase's auth schema handled at the database level.
+    """
+
+    __tablename__: str = "profiles"
+
+    id: Mapped[uuid.UUID] = mapped_column(
+        UUID(as_uuid=True),
+        primary_key=True,
+    )
+    username: Mapped[str] = mapped_column(
+        String(30),
+        unique=True,
+        nullable=False,
+        index=True,
+    )
+    display_name: Mapped[str | None] = mapped_column(
+        String(50),
+        nullable=True,
+    )
+    avatar_url: Mapped[str | None] = mapped_column(
+        Text,
+        nullable=True,
+    )
+    bio: Mapped[str | None] = mapped_column(
+        String(200),
+        nullable=True,
+    )