refactor: Replace inline call_type Literals with CallTypesLiteral (17 files)

[Chesars]

Summary

Closes #16495

This PR continues the refactoring started in #16362 (commit c96da44) by replacing inline Literal type definitions for call_type parameters with the centralized CallTypesLiteral import from litellm.types.utils across 17 additional files.

Changes

• Added CallTypesLiteral import to 17 files
• Removed duplicate inline Literal[...] definitions
• Net reduction: 295 lines of code removed (45 insertions, 340 deletions)

Benefits

• DRY Principle: Eliminates duplication of the same type definition across multiple files
• Maintainability: Single source of truth for call_type values
• Type Safety: Maintains full type checking while using centralized definition
• Consistency: Follows the same pattern from commit c96da44

Files Modified (17 total)

• litellm/cost_calculator.py
• litellm/router.py (largest change: 67 lines removed)
• litellm/litellm_core_utils/llm_response_utils/get_formatted_prompt.py
• 14 guardrail hooks:
  • litellm/proxy/guardrails/guardrail_hooks/aporia_ai/aporia_ai.py
  • litellm/proxy/guardrails/guardrail_hooks/azure/prompt_shield.py
  • litellm/proxy/guardrails/guardrail_hooks/azure/text_moderation.py
  • litellm/proxy/guardrails/guardrail_hooks/custom_guardrail.py
  • litellm/proxy/guardrails/guardrail_hooks/grayswan/grayswan.py
  • litellm/proxy/guardrails/guardrail_hooks/guardrails_ai/guardrails_ai.py
  • litellm/proxy/guardrails/guardrail_hooks/lakera_ai.py
  • litellm/proxy/guardrails/guardrail_hooks/lasso/lasso.py
  • litellm/proxy/guardrails/guardrail_hooks/model_armor/model_armor.py
  • litellm/proxy/guardrails/guardrail_hooks/openai/moderations.py
  • litellm/proxy/guardrails/guardrail_hooks/panw_prisma_airs/panw_prisma_airs.py
  • litellm/proxy/guardrails/guardrail_hooks/pillar/pillar.py
  • litellm/proxy/guardrails/guardrail_hooks/tool_permission.py
  • litellm/proxy/hooks/prompt_injection_detection.py

Example

# Before:
call_type: Literal[
    "completion",
    "text_completion",
    "embeddings",
    # ... more values
]

  # After:
  call_type: CallTypesLiteral

Testing

• Type checking remains intact (MyPy compatible)
• No runtime behavior changes (type hints are not enforced at runtime)
• All existing tests should pass without modification

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