feat(api): add short_id column for consistent LLM UUID handling

Resolves validation failures where LLM fabricated full UUIDs from 8-char
prefixes shown in context, causing 'unknown product_id' errors.

Root Cause Analysis:
- Context showed 8-char short IDs: '77cbf37c' (Phase 2 optimization)
- Function tool returned full UUIDs: '77cbf37c-3830-4927-...'
- LLM saw BOTH formats, got confused, invented UUIDs for final response
- Validators rejected fabricated UUIDs as unknown products

Solution: Consistent 8-char short_id across LLM boundary:
1. Database: New short_id column (8 chars, unique, indexed)
2. Context: Shows short_id (was: str(id)[:8])
3. Function tools: Return short_id (was: full UUID)
4. Translation layer: Expands short_id → UUID before validation
5. Database: Stores full UUIDs (no schema change for existing data)

Changes:
- Added products.short_id column with unique constraint + index
- Migration populates from UUID prefix, handles collisions via regeneration
- Product model auto-generates short_id for new products
- LLM contexts use product.short_id consistently
- Function tools return product.short_id
- Added _expand_product_id() translation layer in routines.py
- Integrated expansion in suggest_routine() and suggest_batch()
- Validators work with full UUIDs (no changes needed)

Benefits:
✅ LLM never sees full UUIDs, no format confusion
✅ Maintains Phase 2 token optimization (~85% reduction)
✅ O(1) indexed short_id lookups vs O(n) pattern matching
✅ Unique constraint prevents collisions at DB level
✅ Clean separation: 8-char for LLM, 36-char for application

From production error:
  Step 1: unknown product_id 77cbf37c-3830-4927-9669-07447206689d
  (LLM invented the last 28 characters)

Now resolved: LLM uses '77cbf37c' consistently, translation layer
expands to real UUID before validation.

backend/alembic/versions/27b2c306b0c6_add_short_id_column_to_products.py

@@ -0,0 +1,83 @@
+"""add short_id column to products
+
+Revision ID: 27b2c306b0c6
+Revises: 2697b4f1972d
+Create Date: 2026-03-06 10:54:13.308340
+
+"""
+
+from typing import Sequence, Union
+
+import sqlalchemy as sa
+
+from alembic import op
+
+# revision identifiers, used by Alembic.
+revision: str = "27b2c306b0c6"
+down_revision: Union[str, Sequence[str], None] = "2697b4f1972d"
+branch_labels: Union[str, Sequence[str], None] = None
+depends_on: Union[str, Sequence[str], None] = None
+
+
+def upgrade() -> None:
+    """Upgrade schema.
+
+    Add short_id column (8-char prefix of UUID) for LLM token optimization.
+    Handles collisions by regenerating conflicting short_ids.
+    """
+    # Step 1: Add column (nullable initially)
+    op.add_column("products", sa.Column("short_id", sa.String(8), nullable=True))
+
+    # Step 2: Populate from existing UUIDs with collision detection
+    connection = op.get_bind()
+
+    # Get all products
+    result = connection.execute(sa.text("SELECT id FROM products"))
+    products = [(str(row[0]),) for row in result]
+
+    # Track used short_ids to detect collisions
+    used_short_ids = set()
+
+    for (product_id,) in products:
+        short_id = product_id[:8]
+
+        # Handle collision: regenerate using next 8 chars, or random
+        if short_id in used_short_ids:
+            # Try using chars 9-17
+            alternative = product_id[9:17] if len(product_id) > 16 else None
+            if alternative and alternative not in used_short_ids:
+                short_id = alternative
+            else:
+                # Generate random 8-char hex
+                import secrets
+
+                while True:
+                    short_id = secrets.token_hex(4)  # 8 hex chars
+                    if short_id not in used_short_ids:
+                        break
+
+            print(f"COLLISION RESOLVED: UUID {product_id} → short_id {short_id}")
+
+        used_short_ids.add(short_id)
+
+        # Update product with short_id
+        connection.execute(
+            sa.text("UPDATE products SET short_id = :short_id WHERE id = :id"),
+            {"short_id": short_id, "id": product_id},
+        )
+
+    # Step 3: Add NOT NULL constraint
+    op.alter_column("products", "short_id", nullable=False)
+
+    # Step 4: Add unique constraint
+    op.create_unique_constraint("uq_products_short_id", "products", ["short_id"])
+
+    # Step 5: Add index for fast lookups
+    op.create_index("idx_products_short_id", "products", ["short_id"])
+
+
+def downgrade() -> None:
+    """Downgrade schema."""
+    op.drop_index("idx_products_short_id", table_name="products")
+    op.drop_constraint("uq_products_short_id", "products", type_="unique")
+    op.drop_column("products", "short_id")