Validate that all variables in template content are valid Pydantic fields.

This endpoint checks:

1. All {{variable}} references are extracted
2. Each variable corresponds to a field in LoadSchema or CarrierSchema
3. Nested paths are valid (e.g., load.customer.name)
4. Array access is valid (e.g., load.stops.0.city)

Returns validation result with any errors found.

Use this for:

• Real-time validation in template editor
• Pre-save validation
• Displaying helpful error messages to users