Prefer init-provided system instruction in Grok Realtime

Add system_instruction parameter to the Grok Realtime adapter's
get_llm_invocation_params() and call _resolve_system_instruction() to
prefer init-provided over context-provided system instructions and
warn on conflicts. Previously context-provided took precedence.

Update the Grok Realtime example to use settings.system_instruction
instead of session_properties.instructions.

examples/foundational/51-grok-realtime.py

@@ -172,23 +172,6 @@ async def run_bot(transport: BaseTransport, runner_args: RunnerArguments):
     session_properties = SessionProperties(
         # Voice options: Ara, Rex, Sal, Eve, Leo
         voice="Ara",
-        # System instructions
-        instructions="""You are a helpful and friendly AI assistant powered by Grok.
-
-You have access to several tools:
-- Weather information
-- Current time
-- Restaurant recommendations
-- Web search (built-in)
-- X/Twitter search (built-in)
-
-Your voice and personality should be warm and engaging. Keep your responses
-concise and conversational since this is a voice interaction.
-
-If the user asks about current events or news, use web search.
-If they ask about what people are saying on social media, use X search.
-
-Always be helpful and proactive in offering assistance.""",
         # Grok-specific built-in tools can be added here:
         # tools=[
         #     WebSearchTool(),  # Enable web search
@@ -200,6 +183,22 @@ Always be helpful and proactive in offering assistance.""",
     llm = GrokRealtimeLLMService(
         api_key=os.getenv("GROK_API_KEY"),
         settings=GrokRealtimeLLMService.Settings(
+            system_instruction="""You are a helpful and friendly AI assistant powered by Grok.
+
+    You have access to several tools:
+    - Weather information
+    - Current time
+    - Restaurant recommendations
+    - Web search (built-in)
+    - X/Twitter search (built-in)
+
+    Your voice and personality should be warm and engaging. Keep your responses
+    concise and conversational since this is a voice interaction.
+
+    If the user asks about current events or news, use web search.
+    If they ask about what people are saying on social media, use X search.
+
+    Always be helpful and proactive in offering assistance.""",
             session_properties=session_properties,
         ),
     )

src/pipecat/adapters/services/grok_realtime_adapter.py

@@ -50,18 +50,26 @@ class GrokRealtimeLLMAdapter(BaseLLMAdapter):
         """Get the identifier used in LLMSpecificMessage instances for Grok Realtime."""
         return "grok-realtime"
 
-    def get_llm_invocation_params(self, context: LLMContext) -> GrokRealtimeLLMInvocationParams:
+    def get_llm_invocation_params(
+        self, context: LLMContext, *, system_instruction: Optional[str] = None
+    ) -> GrokRealtimeLLMInvocationParams:
         """Get Grok Realtime-specific LLM invocation parameters from a universal LLM context.
 
         Args:
             context: The LLM context containing messages, tools, etc.
+            system_instruction: Optional system instruction from service settings.
 
         Returns:
             Dictionary of parameters for invoking Grok's Voice Agent API.
         """
         messages = self._from_universal_context_messages(self.get_messages(context))
+        effective_system = self._resolve_system_instruction(
+            messages.system_instruction,
+            system_instruction,
+            discard_context_system=True,
+        )
         return {
-            "system_instruction": messages.system_instruction,
+            "system_instruction": effective_system,
             "messages": messages.messages,
             "tools": self.from_standard_tools(context.tools) or [],
         }

src/pipecat/services/grok/realtime/llm.py

@@ -607,11 +607,15 @@ class GrokRealtimeLLMService(LLMService):
         adapter: GrokRealtimeLLMAdapter = self.get_llm_adapter()
 
         if self._context:
-            llm_invocation_params = adapter.get_llm_invocation_params(self._context)
+            llm_invocation_params = adapter.get_llm_invocation_params(
+                self._context, system_instruction=self._settings.system_instruction
+            )
 
             if llm_invocation_params["tools"]:
                 settings.tools = llm_invocation_params["tools"]
 
+            # The adapter resolves conflicts between init-provided and
+            # context-provided system instructions (preferring init-provided).
             if llm_invocation_params["system_instruction"]:
                 settings.instructions = llm_invocation_params["system_instruction"]