server: fix format of streamed tool call deltas (diff name, fix id location)

[ochafik]

Fix format of tool call diffs, now much more conformant to the OAI format:

• Define id on the tool_call itself, not inside tool_call.function.id
• Return tool_call.function.name as a delta, not repeated over and over.
• Define tool_call.type ("function")
• Return empty tool_call.arguments on the first tool call delta

Fixes #13774 (also reported here cc/ @bgs4free @Rane2021 @TheTerrasque @making @PrideIsLife @tctien342 )

Note this still sends the tool name in one go, as both OpenAI & Anthropic APIs seem to do (which is probably what confused me initially)

Follow up to #12379

Example of outputs

clear && curl http://localhost:8080/v1/chat/completions \
  -H "Content-Type: application/json" \
  -d '{
    "model": "gpt-4o",
    "tools": [{
          "type": "function",
          "function": {
              "name": "get_current_weather",
              "description": "Get the current weather",
              "parameters": {
                  "type": "object",
                  "properties": {
                      "location": {
                          "type": "string",
                          "description": "The city and state, e.g. San Francisco, CA"
                      },
                      "format": {
                          "type": "string",
                          "enum": ["celsius", "fahrenheit"],
                          "description": "The temperature unit to use. Infer this from the users location."
                      }
                  },
                  "required": ["location", "format"]
              }
          }
      }, {
          "type": "function",
          "function": {
              "name": "get_n_day_weather_forecast",
              "description": "Get an N-day weather forecast",
              "parameters": {
                  "type": "object",
                  "properties": {
                      "location": {
                          "type": "string",
                          "description": "The city and state, e.g. San Francisco, CA"
                      },
                      "format": {
                          "type": "string",
                          "enum": ["celsius", "fahrenheit"],
                          "description": "The temperature unit to use. Infer this from the users location."
                      },
                      "num_days": {
                          "type": "integer",
                          "description": "The number of days to forecast"
                      }
                  },
                  "required": ["location", "format", "num_days"]
              }
          }
      }],
    "messages": [
      {"role": "system", "content": "You are a function calling AI model. You are provided with function signatures within <tools></tools> XML tags. You may call one or more functions to assist with the user query. Do not make assumptions about what values to plug into functions. Here are the available tools:"},
      {"role": "user", "content": "what is the weather going to be like in San Francisco and Glasgow over the next 4 days"}
    ],
    "stream": true
  }'

data: {"choices":[{"finish_reason":null,"index":0,"delta":{"role":"assistant","content":null}}],"created":1748263544,"id":"chatcmpl-xxesoUemboS3eSaTCzm7PRweLJGrESU2","model":"gpt-4o","system_fingerprint":"b5496-a7e6f3941","object":"chat.completion.chunk"}

data: {"choices":[{"finish_reason":null,"index":0,"delta":{"tool_calls":[{"index":0,"id":"iL1vo9XXQNwkXzcKwyYF4wpGwvRF5HAP","type":"function","function":{"name":"get_current_weather","arguments":""}}]}}],"created":1748263544,"id":"chatcmpl-xxesoUemboS3eSaTCzm7PRweLJGrESU2","model":"gpt-4o","system_fingerprint":"b5496-a7e6f3941","object":"chat.completion.chunk"}

data: {"choices":[{"finish_reason":null,"index":0,"delta":{"tool_calls":[{"index":0,"function":{"arguments":"{"}}]}}],"created":1748263544,"id":"chatcmpl-xxesoUemboS3eSaTCzm7PRweLJGrESU2","model":"gpt-4o","system_fingerprint":"b5496-a7e6f3941","object":"chat.completion.chunk"}

data: {"choices":[{"finish_reason":null,"index":0,"delta":{"tool_calls":[{"index":0,"function":{"arguments":"\""}}]}}],"created":1748263544,"id":"chatcmpl-xxesoUemboS3eSaTCzm7PRweLJGrESU2","model":"gpt-4o","system_fingerprint":"b5496-a7e6f3941","object":"chat.completion.chunk"}

data: {"choices":[{"finish_reason":null,"index":0,"delta":{"tool_calls":[{"index":0,"function":{"arguments":"location"}}]}}],"created":1748263544,"id":"chatcmpl-xxesoUemboS3eSaTCzm7PRweLJGrESU2","model":"gpt-4o","system_fingerprint":"b5496-a7e6f3941","object":"chat.completion.chunk"}

data: {"choices":[{"finish_reason":null,"index":0,"delta":{"tool_calls":[{"index":0,"function":{"arguments":"\":"}}]}}],"created":1748263544,"id":"chatcmpl-xxesoUemboS3eSaTCzm7PRweLJGrESU2","model":"gpt-4o","system_fingerprint":"b5496-a7e6f3941","object":"chat.completion.chunk"}

data: {"choices":[{"finish_reason":null,"index":0,"delta":{"tool_calls":[{"index":0,"function":{"arguments":"\""}}]}}],"created":1748263544,"id":"chatcmpl-xxesoUemboS3eSaTCzm7PRweLJGrESU2","model":"gpt-4o","system_fingerprint":"b5496-a7e6f3941","object":"chat.completion.chunk"}

...

[CISC]

LGTM