Add custom headers support for API Management integration

This change adds support for custom HTTP headers in AI inference requests,
enabling integration with API Management platforms (Azure APIM, AWS API
Gateway, Kong, etc.) and custom request routing/tracking.

Features:
- New 'custom-headers' input supporting both YAML and JSON formats
- Auto-detection of input format for better UX
- Header name validation (alphanumeric, hyphens, underscores)
- Automatic masking of sensitive headers in logs
- Full backward compatibility (optional parameter)

Changes:
- Added parseCustomHeaders() function in helpers.ts
- Updated InferenceRequest interface with optional customHeaders field
- Modified simpleInference() and mcpInference() to pass headers to OpenAI client
- Added 18 comprehensive test cases
- Updated documentation with examples and use cases

All 80 tests passing. Zero breaking changes.

__tests__/inference.test.ts

@@ -75,6 +75,49 @@ describe('inference.ts', () => {
         max_tokens: 100,
         model: 'gpt-4',
       })
+
+      // Verify OpenAI client was initialized with empty custom headers
+      expect(mockOpenAIClient).toHaveBeenCalledWith({
+        apiKey: 'test-token',
+        baseURL: 'https://api.test.com',
+        defaultHeaders: {},
+      })
+    })
+
+    it('includes custom headers in OpenAI client', async () => {
+      const requestWithHeaders = {
+        ...mockRequest,
+        customHeaders: {
+          'X-Custom-Header': 'custom-value',
+          'Ocp-Apim-Subscription-Key': 'secret123',
+        },
+      }
+
+      const mockResponse = {
+        choices: [
+          {
+            message: {
+              content: 'Response with headers',
+            },
+          },
+        ],
+      }
+
+      mockCreate.mockResolvedValue(mockResponse)
+
+      const result = await simpleInference(requestWithHeaders)
+
+      expect(result).toBe('Response with headers')
+
+      // Verify OpenAI client was initialized with custom headers
+      expect(mockOpenAIClient).toHaveBeenCalledWith({
+        apiKey: 'test-token',
+        baseURL: 'https://api.test.com',
+        defaultHeaders: {
+          'X-Custom-Header': 'custom-value',
+          'Ocp-Apim-Subscription-Key': 'secret123',
+        },
+      })
     })
 
     it('handles null response content', async () => {
@@ -186,6 +229,50 @@ describe('inference.ts', () => {
       expect(callArgs.response_format).toBeUndefined()
       expect(callArgs.model).toBe('gpt-4')
       expect(callArgs.max_tokens).toBe(100)
+
+      // Verify OpenAI client was initialized with empty custom headers
+      expect(mockOpenAIClient).toHaveBeenCalledWith({
+        apiKey: 'test-token',
+        baseURL: 'https://api.test.com',
+        defaultHeaders: {},
+      })
+    })
+
+    it('includes custom headers in MCP inference', async () => {
+      const requestWithHeaders = {
+        ...mockRequest,
+        customHeaders: {
+          serviceName: 'test-service',
+          'X-Team': 'engineering',
+        },
+      }
+
+      const mockResponse = {
+        choices: [
+          {
+            message: {
+              content: 'MCP response with headers',
+              tool_calls: null,
+            },
+          },
+        ],
+      }
+
+      mockCreate.mockResolvedValue(mockResponse)
+
+      const result = await mcpInference(requestWithHeaders, mockMcpClient)
+
+      expect(result).toBe('MCP response with headers')
+
+      // Verify OpenAI client was initialized with custom headers
+      expect(mockOpenAIClient).toHaveBeenCalledWith({
+        apiKey: 'test-token',
+        baseURL: 'https://api.test.com',
+        defaultHeaders: {
+          serviceName: 'test-service',
+          'X-Team': 'engineering',
+        },
+      })
     })
 
     it('executes tool calls and continues conversation', async () => {